Though I've ranted about Half-Life 2 before, I still like Source engine based commercial games especially graphically and looking over the Wikipedia entries:
http://en.wikipedia.org/wiki/Id_Tech_4
http://en.wikipedia.org/wiki/Source_(game_engine)
I just feel like Source might be slightly better.
(There does seem to be one big difference from what I can tell. Source is Direct3D on Microsoft platforms, while id Tech 4 is a pure OpenGL engine. Not sure how this might translate for you though.)
Well, it's a plus if I can work on linux, but anyway, I don't have the money to pay UE4, though this will be just for educational purposes.
Could your question be stated as "free to use FPS engine with strong C++ API and Linux support"?
There's a lot of choices for that, honestly.
If free-to-use isn't a hard requirement, then Unreal Engine 4 excels with it's fantastic C++ API and very helpful game (including AI) framework classes. Linux export is supported, native Linux compilation (and editor) coming soon.
Sort of! but the answer is the same as before, free-to-use is a hard requirement since this is for educational purposes and not for making money with it.
I'm looking for some already made FPS that I can modify, just that. So this may be not a good post name, mainly because Source or idTech4 are not FPS, but engines. Also, if it would be easier to make a fps from scratch using some engine, than modding an already made game, I'm okay with that, but I currently think it would be easier to modify an existing one.
EDIT: ease of use is preferred.