Not really. Plan II has small class sizes and is in the honors dorms (the ABC dorms), which function a lot like a residential college at Rice.
Plan II is cheaper, plus you'd be in Austin rather than Houston and have real sports.
Rice has a better reputation, is a lot smaller and comfortable, and is very "quirky."
Rice is a bit more prestigious, but UT's plan II is a great deal for its cost. Where is the $20k number coming from? Are you out of state? Because UT is more like $13k for in-state students as a total.