But it's when we get to JLA/Avengers that problems crop up. This crossover is of the first kind - inter-dimensional travel - and is canon, as it had repurcussions in mainstream DC, but it posits that any merging of two distinct universes results in widespread cataclysm and destruction....none of which was evident during the earlier mergers which must have occurred. So, from an in-story perspective, how to account for this?
I'm just spitballing from memory here, but the JLA/Avengers was arguably the first time that parallel earths merged "post-crisis." The whole point of crisis was that dozens of parallel earths got merged for good and supposedly there weren't any more. Perhaps, the arrival/discovery of additional parallel earths was of earths where merger had repercussions not seen in the earlier merger[s].
As for my favorites, the Shooter-written Superman/Spider-man is probably still my favorite, followed closely by JLA/Avengers.
I also enjoyed Batman/Capt. America and one of the Batman/Spider-man team-ups, though I can't remember which one.
In the case of the Batman/Spiderman book, it was less the story or art and more the moment where Batman gave Spidey a "look" in the Batmobile over some of his usual Parker wisecracks and Peter immediately got embarrassed and apologized to "Batman, sir." I liked it because it made sense for the characters, insofar as Peter is/was about the same age as Dick Greyson and you'd expect him and Batman to end up in a similar dynamic because of their ages.