Thermal resistance, Junction−to−Ambient (\$ϕ_{JA}\$) of NCP1117 voltage regulator is 160 °C/W and thermal resistance of AMS1117 voltage regulator is 90 °C/W. Remaining specifications are almost same for both regulators. Which of them is preferable?
What is the role of thermal resistance while choosing a voltage-regulator?
The thermal resistance impacts how hot it will get under load, and as such, the power that can be dissipated inside of the device. If you are really pushing the limit of these devices, you would want the one with the lowers thermal resistance. Keep in mind though that this thermal resistance can be dependent on layout of the pcb, as well as the copper thickness.
It could be that one of the two parts has a bad junction-to-ambient because the writers of one of the datasheets decided to specify the junction-to-ambient with a given pcb heatsink, while the others did not.
All in all, it is very dependent on design constraints. Often you would just want to go with the cheapest part that will meet your specifications (and is available and from a manufacturer you trust etc.)
From data sheets, maximum junction temperature is 175°C for NCP1117 and 125°C for AMS1117.
So if you plug these numbers in to the formula with a 20°C ambient temperature, the NCP1117 (0.969W) will dissipate less power than the AMS1117 (1.167W).
$$ P_D = \frac {T_{J (Max)} - T_A} {R_{\theta JA}}$$
Which makes the NCP1117 the better part, but this is only relevant if you are pushing the device at maximum power. Better usually costs more.
Junction to ambient figure means in simple terms how much does the semiconductor heat up in relation to ambient temperature given a specific power dissipation in watts. so \$100 \frac{°C}W\$ \$T_a=25°C\$ with 1W of dissipation leads to 125°C temperature.
This obviously depends on available copper area to dissipate heat, copper thickness, thermal vias to use the opposite side of the PCB for heat dissipation and so on. You may even use a solder-on heatsink for SMD chips which boost the dissipation a fair bit. Or the more traditional glue-on solution.
In short, less thermal resistance equals better but as others pointed out, the better thermal conductive part has much lower max temperature so it's a bit of give and take.
A better metric than \$R_{\phi JA}\$ would be \$R_{\phi JC}\$, temperature from junction to case (or pad). After all, at that point it becomes your job to dissipate the heat one way or another. Plus it's not up to whatever PCB technology / pad style you're using.
