In the case of apps that are available on both f-droid and on the play store, the difference is that the f-droid versions will be compiled without google play services. This can limit functionality (for example, receiving notifications while the phone is asleep), but does increase privacy somewhat.

Significantly, there is very little overlap in the apps available on f-droid and the apps available on the google play store. Most play store apps siphon data, and most f-droid apps don't.