IMO I think he fits more in the FF than the Avengers, he's very closely tied to the FF and has a more family dynamic with them. He geeks out with Reed, jokes around with Ben and Johnny, has heart to heart talks with Sue (and also jokes with her too).

Although I have to say the era were he was living in Avengers Tower with MJ and Aunt May was probably one of my favorite Spidey/Avenger moments (if only for Jarvis/May and Pete and MJ having training sessions with Steve).