Everyone else's mileage will vary, but honestly? I find "JLAvengers" one of my favourite comics of all time. It's just so... awesome. There's no other word for it. It's big and it's loud and Buseik does such an excellent job as story-teller it leaves me breathless.
(not to mention the moment where, as they all set out to explore the MU, Batman tells the rest of the League not to interfere, then spends 20 minutes beating the stuffing out of the Punisher, in a 'fight' that's so one-sided it happens off-camera and Plastic Man jokes about it afterwards)
I lean more towards DC anyway, so I was quite happy with how the JLA vs Avengers aspects played out (even though it pretty much ended as a tie, although the JLA won by plot-mandated technicality) -- except for that one bit. Thor should've beat Superman. Weaknesses to magic aren't great when you're fighting a god.
But that bit in book 4 when Superman charges into battle with Captain America's shield in one hand and Mjolnir in the other -- that's like porn for me. So it's all good, heh.