I think the game-changer here is Strange. On any given day he'd be causing anyone on the other team all sorts of bother. Throw in a week of prep-time for him, and the pain-factor goes up all the way to eleven I think. Unless someone argues that Batman plus a week of prep equals insta-win via some sort of anti-magic utility belt nonsense Bruce cobbles together.
I'm still going with the Avengers. Everyone else is quite well-matched but Strange tips it. IMO
Unless Batman uses that time to seek out Dr Fate or (maybe more importantly since he's nastier) John Constantine, there's really nothing much they can do about Dr Strange.
Now, I can come up with a scenario where I can use the Flash to win, but I don't feel like discussing attoseconds . More importantly, I can come up with easier scenarios where I can use Strange to win. Especially with prep.
IMO this depends a lot on how good a day Strange is having. On a good day he can tip the balance to the WAs, especially given a week of prep. But on an average to bad day not so much.
The classic DC lineup really is a powerhouse in strength, power, weapons, and speed though. And they have the teamwork angle down.
It also comes down to exactly what limit is placed on the prep. They can't call in other characters obviously but is their prep also limited to high herald? - there's super tech, objects of power etc that these guys could get access to in a week such as motherboxes, high end artifacts, Kryptonian tech, Oan tech, New Gods tech and so on.
Tough fight, but I'm giving a majority to the JLA.