Does having a large penis make you a better lover and does it satisify your woman more than an average size dick?

That depends on who you meet! Some women like them big, others like them smaller/more average.

But even if a woman like it big, you can satisfy just as much if you do it right! Don't focus only on the vagina, give the breasts and her whole body some nice attention!

Don't get hung up on your penis, it doesn't really matter in the end. Unless you have a micropenis, you won't have any problems!