If Spiderman bonded with the Symbiote then Spiderman would become much stronger than he currently is...Technically in the comics, the symbiote didn't actually make him stronger, it just gave him all the symbiote's abilities that Venom normally uses, the webs, stealth, and defensive capabilities.
If they have any sort of cross over involving different marvel teams, then it would be the newly introduced Fantastic Four because Reed Richards is the one who helps Spiderman understand the symbiote and he also helps him get rid of the symbiote. (in the comics)
If a different character obtained the symbiote various things could happen. If the symbiote was originally on Peter Parker, then whoever obtained the symbiote would also retain some of Spiderman's types of powers...just like Brock got when he became Venom. If not, then odds are the symbiote would mimic that hero's particular abilities and the next host would have powers resembling the original owner.
Needless to say, if Wolverine got the symbiote instead of Eddie Brock...then Spiderman would undoubtably be killed because the symbiote would rip Wolvy's head up with thoughts of wanting to kill Spiderman until Wolverine went to kill Spiderman, but unlike any other time the two have met....Wolverine would be able to win.