This doesn't really effect performance IE a 16 GB device will perform about as well as a 64 GB device but in smaller storage device memory is at a premium. Apps, music, etc. fill it up very fast. If you have a computer with iTunes and don't mind micromanaging this is no biggie but is very annoying otherwise.
If you use a lot of different apps, I strongly recommend a larger capacity phone bc you are not going to want to be uninstalling and reinstalling your apps all the time.
But remember you cannot supplement or upgrade this later. What you get is what you have so strongly consider if saving money on smaller capacity phone is worth not ever having the option to increase it for the life of the phone.
This is one area where I like Android. Wish iOS could use microSD then the discussion would be meaningless
