iPhone 14 vs 13: Performance and Battery
iPhones generally perform very well in terms of daily use, gaming and so on, and the iPhone 14 and iPhone 13 are no match for the performance. Both are powered by Apple's powerful A15 Bionic processor, but don't be fooled as the iPhone 14 has a 5-core GPU for better gaming performance compared to the iPhone 13's 4-core GPU. This doesn't mean you you will notice any difference in reality.
That said, they can both play Call of Duty with no issues, no issues, no lag, it just works really well so I wouldn't consider it a deal breaker when it comes to upgrading from 13 to 14.
Of course, performance isn't just about processing power and gaming ability, yes, it's fluid and very smooth, but how long can you use it? On paper the iPhone would get 14 to 20 hours of video playback, 16 hours of streaming Netflix for example and 80 hours of audio playback, the iPhone 13 on the other hand would get 19 hours of video playback, 15 hours of streaming videos and 75 hours of audio playback, so technically the iPhone would 14 should last a little longer, but in reality this varies depending on your usage and is very similar in terms of overall performance, so there's no big advantage here.
Elsewhere on the iPhone 14 you get SOS satellite communications and in-car collision detection, but unless you're in remote locations where you need an SOS satellite connection it doesn't really matter, and most cars these days have emergency crash detection, so I wouldn't worry too much about that.