Unless Conner has the Apple Geralt wins. Geralt is stronger/faster and has magical powers and he can alter time as well (Heliotrop Sign) In Witcher 1 he was playing around with a Striga like it was nothing, he also can enhance his abilities like strength and speed by drinking potions. Like Conner, Geralt has fought assassins and soldiers but in addition to that he also fought against Witchers, Monsters and Sorcerers and lived to tell the tell, so i say geralt also has more exp than Conner + Geralt IIRC is very old (doesn't age like humans or something like that).
Yes. Like i already said Geralt has fought much more diverse and powerfull opponents than Conner did. Geralt also has multiple styles of fighting, he can adjust his fighting style to handle heavy/small/fast or groups of enemies. Geralt also fought against other of his kind and won. There are some comics and books ofcourse than go deeper into this but i've not read those yet. Minus Geralt's swordsmanship he also had Magic on his side and is psychically supirior than Conner due to being a Witcher and he can enchance this futher by his Alchemy.