The 16gb vs 32gb is the local data storage capacity. It does affect how many matches you can have saved on device, but even for 16gb it is a lot of matches. Also, in both cases local storage is extendable by an external SD card and we do recommend to use that to save local score log. So, you aren’t going to see performance difference for different storage capacity.
However there are several models/generations of both Fire 7 and Fire 8 devices. Newer models have beefier CPU and more memory (RAM) and that does make things run faster on those new devices. You can find somewhat complete technical specs reference for Fire device models at Fire HD - Wikipedia
Bottom line. If you are buying Fire 7 - prefer the latest generation model (2022). For Fire 8 - either get the latest generation (2022, will be released on October 19, 2022) or one before (2020, for this one you can often find refurbished ones on sale).