You have to run through the calculations and available hardware in each individual case to decide what is best.
For example, you likely would not want to use a '24-bit' converter with a real ENOB of maybe 19 bits (at a very low sample rate) to measure a low-level signal when a much cheaper and higher performance 12-bit converter would do that job with an amplifier.
Higher sample rate results in more noise, so at very high sample rates there really isn't much choice or the cost and maybe power consumption difference is too painful.
Passive RC filters may work okay at low levels, but if you want to insert an analog active filter you will introduce additional errors at low levels. It's not possible to do the filtering in software if you don't first anti-alias and/or oversample at a high enough rate (theoretically 2x the highest noise component frequency, but practically a fair bit more than that depending on how complex your filter can be) to avoid significant amounts of noise being aliased into the signal bandwidth.
There may well be cases where it makes the most sense to avoid amplification and (especially) offset, such as 4~20mA process signals where a 25mA full scale ADC is likely a better approach than using the whole range of a similar converter, trading off about 1/3 of the resolution to avoid the precision offset and amplification. A similar trade-off can be used to avoid analog calibration- if it's desirable to avoid expensive high-precision resistors, voltage reference and/or trimpots- the calibration can be done in software, at the expense of some resolution. At some level of required system accuracy you will not be able to buy parts accurate enough at just about any price.
If you remove the constraint of cost (and maybe power consumption)- you don't care if you use a $10 part to do a $0.50 job, and the job is not all that difficult to begin with, then it makes sense in a lot more cases.
And, of course, there's no real difference between a chip that integrates the amplifier and an external amplifier from the system point of view- if you have an amplifier, you have an amplifier. The on-board PGA may be better or worse than one you can supply externally in one respect or another, depending on your constraints, skills and available components.