Both GNOME and KDE are first-class DEs in Fedora - stability is a non issue. You can install both if you want and select your choice at the login screen to just switch back and forth. The only thing you might want to keep in mind is that both have their own prpgrams, like file managers for example, so you’ll have two programs for the same task.
Performance is a wash, really, with a halfway modern setup. Your browser will be consuming way more resources than the desktop by far.
Compatibility is also a non issue nowadays, both implement the Freedesktop standard and are fully compatible with each other.
I’m pretty sure that the installer is the same for all major spins.