Source:IGN

If you never played Rainbow Six 3, you should be ashamed of yourself. But just for context, Rainbow Six 3: Black Arrow and its predecessor are first-person tactical shooters. The tactical aspect comes from the ten missions, where (when playing alone) you'll command three AI comrades. The commands are very simple. You can tell your teammates where to go, get them to follow and cover, and use several options to breach doors and clear rooms. The commands remain as simple as in Black Arrow and your AI teammates aren't any smarter. It's when you go multiplayer that Black Arrow truly comes alive.
With the exception of the new Lone Rush mode, every game mode in Black Arrow can be played cooperatively. The missions can be tackled offline with a buddy in split-screen, with up to four players through System Link, or with four people over Xbox Live. Terrorist AI is still pretty basic and with no armor it's a snap to take out the baddies. However, they are smarter than in the first Rainbow Six 3 and will sometimes run off to get backup and generally try to take cover, though some will still run straight at you, guns blazing.

Backward compatability issues

From my personal experiance, none. I had to download 2 differnt times. Once to play the offline, then another to play online correctly. I saw no improvments in graphics on the 360 from the original Xbox.