Thanks for clarifying your question... if I understand you correctly, you'd like to get an op-amp that would run fine on +3V power supply. I've noticed this kind of a minimal rail voltage in the datasheets of the TLC271 or TLC272 (classic op-amps, single output, one or two modules per package) and in the THS4521 (fully differential op-amp, and a broadband model BTW).
Note that 3V in general are a pretty low supply voltage, considering what voltage a simple constant current source needs to operate, and how complex the internals of an op-amp can be... this requirement is non-trivial to meet.
Regarding your application, I am surprised that simple resistive dividers on the inherent differential input of the BT module did not perform well :-/ What does an op-amp bring, that makes it perform better? A lower drive impedance for the audio input of the BT module?
What kind of noise did you get? Just a higher level of white noise? Or, was it distortion of some sort? Or ingress EMI? If it was anything other than pure white noise, would you care to share a schematic of your pure passive input with resistive dividers? And, how is your diff input wired to the (external) signal source? How were signal reference grounds catered for?
Other than that, I've had instances where a chip datasheet did not contain the whole truth about its audio "ports", and I had to find out the hard way that its diff input was not really a proper diff input, op-amp style - even though the pinout did resemble an op-amp, upon a first casual look. Which would be a valid motivation to handle the diff input externally (convert to single-ended).
You have interesting toys to play with :-)
EDIT: take a look at the following picture.
I've checked the datasheet of your BT module, and it's pretty clear that the signal inputs are properly balanced. I don't see a reason to force them into single-ended mode. Perhaps you just never got the balanced divider just right in the first place.
Low input impedance (differential and against the local ref.gnd) is generally a benefit in terms of noise in the input stage - though if the inputs are some CMOS/JFET, the benefit won't be very significant. I understand that the "microphone" input can be configured for a pretty low gain (-3 dB ?) and effectively turn into a line-level input. I'd expect the chip's own input noise to be minuscule with the input gain dialed all the way down.
If you're after a good bass response, try increasing the coupling capacitors in the signal path. The lower the resistance of the attenuator/divider, the larger the capacitors should be - consider the cut-off frequency of the resulting RC low-pass filter. This applies especially to the coupling capacitors at the board's input - less likely a problem with the coupling caps at the codec chip input (the internal biasing resistance will likely be relatively high).
If your signal source actually has PWM output, you're possibly in for some "hard cheese" :-) A dual-trace oscilloscope would be invaluable to weed this out.
I still believe that the best op-amp in this case is no op-amp :-) especially if you're constrained by the crippling low supply voltage (down to 3V off a single LiIon cell).
Hmm. Unless the balanced input in the codec chip has really poor common mode rejection ratio, and your signal source has a nasty common mode AC component to it - in that case a fast op-amp might help, provided that you can steer in the pretty narrow corridor of valid operation between the supply rails. So if you end up in this configuration, consider attenuating the input signal a little more and increasing the gain in your codec a bit after your discrete op-amp.
All other conditions equal, an op-amp will exhibit relatively lower slew rate (and CMRR) towards the lower end of the permitted supply voltage range :-(
EDIT: In response to your question in the comments, "Also I saw some op-amps with pairs of equal resistors: 1k, 12k, 10k, 25k... which should I use? Or any will work?"
Symmetrical op-amps, such as the THS4521, have two feedback dividers in the basic topology (four resistors total). See also this nice appnote - feel free to skip all the humiliating math, look at the basic topology pictures (the first one on page 6 I guess). The THS4521 also allows you to set the desired "common mode output center potential", using a dedicated pin, independent of the inputs and outputs and feedback - the only rule is, that the center potential should be someplace roughly half-way between the power supply rails, and in the center of your codec chip's input range (individual range per input pin).
Actually a typical op-amp-based "differential amplifier" topology (for balanced to single-ended conversion) also contains two dividers and four resistors total, right? :-) Just like you have demonstrated in your first schematic here.
As for "what resistor values work best" : for audio, the typical values of feedback resistors in op-amp circuits is a couple dozen kiloOhms. For BJT-based op-amp inputs, you'd better aim for low kiloOhms of "circuit input resistance", if your signal source can drive that - it will suppress the own noise of any BJT inputs somewhat. Your AC coupling capacitors will get correspondingly bigger to keep the bass cut-off frequency low, if that's an issue. $$ f_c = \frac{1}{2 \cdot \pi \cdot R \cdot C} $$
In other words, especially the op-amp's input transistors actually matter in terms of own noise, which is further affected by the signal source resistance that they see. But, this mostly matters with BJT's, having a pretty finite input impedance. With CMOS or JFET-based op-amps, going low with the impedance of your surrounding resistors won't help much. Quite the contrary, you won't hamper the input noise much if you go for high resistances (which allows you to use smaller AC coupling capacitors, may decrease power consumption etc) - but don't overstretch that too far, because the circuit may also become more sensitive to EMI ingress.
Today's op-amps have a full totem pole stage on the output (as opposed to an open collector against a pull-up resistor) i.e. they pull both up and down, and have a fairly low output impedance and a pretty good load driving capability. Some bread-and-butter BJT op-amps such as the NE5532 can allow you to drive 32-Ohm earphones directly (preferably from a low rail voltage, like +/- 5V, to keep the heat dissipation in the op-amp at bay). Note that the apparent output impedance of an op-amp is "virtually lowered" by the negative feedback loop, trying to "hammer the output voltage home" (using the op-amp's extreme open-loop gain) - but there are certainly inherent limits to the actual current source/sink capability of an op-amp output totem :-) and also limits to the totem's thermal harm capacity. Some are possibly short-circuit-tolerant (against a centered GND), some may be not.
Note that loud pink noise (rather than sharp white noise) possibly with pops / rattling / distortion mixed in, can be a symptom of RF oscillation someplace in the circuit. You cannot hear the oscillation itself, what you hear is some envelope or average in the audio band.
I wouldn't be surprised if a signal source with class D output would do something along those lines to your line-level ("microphone") input.
EDIT: so we now know exactly what your signal source is. Thanks for the datasheet of the MAX98357. Interestingly, there's a whole lot of stuff, but not a word about the PWM switching frequency, and among all the nice graphs, there's not a single oscillogram of the PWM output - probably considered the sweet secret. Well the true story to me is the chapter called "Filterless Class D Operation", and the sentence about "The device relies on the inherent inductance of the speaker coil and the natural filtering of both the speaker and the human ear to recover the audio component of the square-wave output." Well a standard speaker and the human ear might have mercy with the PWM rectangular output, but certainly not the ADC. Take a look at this image (the source page contains an excellent explanation of class D). You are feeding that rectangle into an ADC. Heh I cannot exclude the possibility that it did indeed sound better through a cheap and slow op-amp :-) But you should get a better result by dedicated filtering, even passive. I have updated my sketch:
The schematic now contains two suggestions of where to put a low-pass filter. The green version places the filter on the signal source PCB, just after the PA chip. The blue version is implemented by just adding two capacitors to the balanced ground-referenced divider just before the bluetooth ADC. Note that the "R" in this blue RC filter is not the 9k1 series resistance, but the 9k1 parallel with the 1k to GND (or so I hope). So the blue capacitors need to be calculated for combination with something just under 1k Ohms.
If you have the possibility, you can implement both the green and blue filters, to gain a roll-off of -40 dB per decade. Or you can implement a cascaded filter in some other fashion. You should not lead the signal over a long distance wiring without filtering at the source. The raw output of the filterless class D amp is a radio frequency rectangle with pretty steep edges.
Hmm. I'm still wondering if the MAX98357 produces some half decent balanced signal, i.e. if both the outputs are switching in sync, just in opposite polarities. Because if for instance one output would always stay clamped low and the other output would PWM high, just exchanging turns upon zero crossings, the result after the filter I suggest would not necessarily be what one would expect. One look with an oscilloscope and all would be clear :-)
And in case that the MAX98357 indeed uses some counter-intuitive modulation with a strong common-mode component, again I would give another thought to your approach with an op-amp, only I'd use a THS4521, bias the output to a midpoint between the supply rails and if I understand the balanced feedback topology correctly (A = R2/R1 , because each polarity is in effect "inverting"), you can just "flip the divider" and turn the differential amp into an "active differential attenuator" :-) The attenuating divider would allow the circuit to operate cleanly with rail-to-rail input (or even beyond the power rails) and the attenuated output would have no problem to stay inside the window bounded by PSU rails. And, the output would already be truly balanced.
And in that case, I'd also certainly RC-filter the output of the MAX98357, I'd just place the capacitor differentially between the signal lines. Maybe with two smaller caps going to ground, not sure (to help the THS4521 keep pace with the slew rate of the common mode part that it would need to cancel out by principle of its operation).
