The Morrisson JLA vs The Busiek era Avengers

Who wins

Grant Morrisson's JLA
Electric Superman
Hippolyta
Aquaman with hook hand
Huntress
Zauriel
Green Lantern Kyle
Martian Manhunter
Batman
'Plastic Man
Steel
Big Barda
Aztek
Green Arrow

vs
Busiek Avengers
Thor
Ionic Wonderman
Vision
Binary
Classic Scarlet Witch
Fire Star
Justice
Silver Claw
Triathelon
Wasp
She Hulk
Giant Man
Extremis Ironman

Each side has 10 hours of prep

JLA. Morrison's JLA was one of, if not the strongest JLA in years.

Edit: Also, you forgot Orion.

Also they have Batman and prep while the other side has Ironman only to do some balancing.

Zauriel vs Asmodel(Spectre)

JLA own.

Does the mention of the writer refer only to the characters on the roster under their pen, or does it refer to their characterization as well?

A big motif of the G-Money JLA was their unbelievable uber-competence at what they do, and how regardless of how insanely powerful a threat was, they could ALWAYS find a way to win.