So first off, a disclaimer: I'm a Director at GameBench, and we make tools for measuring mobile app/game performance (frame rate and other metrics) for a lot of major companies (Rovio, Samsung, Seriously, NaturalMotion etc.) I also have a degree in Game Design.
With regards to target frame rates, there's a few answers here that touch a little on some important points (consistency/stability), but here's what I've learned after nearly 5 years of working in mobile game performance:
Lower frame rate definitely saves battery. This is evident through our own testing (which you can confirm at https://data.gamebench.net) and also as we've seen a lot of device manufacturers actually limit the display refresh rate to as low as 52hz as opposed to the standard 60hz commonly used.
On mobile devices in general, you have the option of selecting from the following target frame rates (this is because they are divisors of the max frame rate - 60 FPS):
- 15 FPS
- 30 FPS
- 45 FPS
- 60 FPS
- 90 FPS
- 120 FPS
Note: 90 and 120 FPS are only available on a few (as of writing this, two) devices.
However, the right target frame rate can only be decided once you have an understanding of the gameplay style and user interaction mechanics you're going to implement.
For a puzzle game where user response times (reactions) or physically realistic animations aren't important, then aim for 15 FPS, the lowest available target. For a fast-paced shooter where users will need quick reaction times, then definitely aim for 60 FPS.
You can completely ignore any advice stating targets like 24 or 25 FPS, and always ensure that when you target a particular frame rate, you stay as close as possible to it during gameplay, or else it will impact the user experience.
All the best, and feel free to reach out if you've got any other mobile performance questions :)