iOS 4.2 will bring Game Center to iPad and yes, it will take advantage of the full screen. You'll get a double column-view instead of single like on iPad, and that means your lists (like friends) will on the left and the detail view (like stats) will be on the right.
What's interesting is that beta 1 currently shows a number of icon-shaped outlines "dealt" card-like across Game Center's game table like UI. They don't show any apps yet, but tapping them does indeed take you to the App Store, and each one to a different game.
UPDATE: The outlines are now icons. Looks like they it just took a while to fully populate them.
Everything else looks to be there and be fully operational, from achievements to leaderboards to games.
November can't come fast enough.