There's 2 types of Team Rabbit that I know, one is T1-style and the other is T2-style.
Both games revolve around just the 1 flag and two teams.
T1-style gives points for successful passes based on the difficulty and style of the pass.
Speed of player grab
Speed of flag velocity
Height of grab
Passer's reversal (tossing with back facing catcher - perfect 180degree gets max points)
Catcher's reversal (catching facing opposite the flag - perfect 180degree gets max points)
Sequence passing
Successful passes get these multipled by 2. Successful interceptions get these multiplied by 2. Caught flags from deaths (suicides or other) are +7.
T2-style gives points for successful passes based on the difficulty and style of pass, but also gives many more points for tossing the flag into the opposing team's goal (much like stylish soccer).
I believe the same factors are used in calculating points for passes as T1 though at different scales, though I played TR2 for very little time.
There were also lots of additions to make the flag play interesting. For example, if you bb the enemy flag carrier, you steal the flag (kidney thief). If you MA your teammate, the flag instantly transfers to you (go-go-gadget). If an enemy MAs the flag carrier, lots of flags pop out but only one is the real one (but if you watch carefully for the trajectory you can see it).
And lastly, the plays were generally named after some top players. For example, speed was graded as 0, +1 (Natural), +2 (Un-Natural), +3 (Super-Natural), +4 (Nothing Left to Prove), since he was the best base capper. A midair grenade kill was a Kermy Kill (after [KoV]Lord Kermit), and so on and so forth.