I have eaten at both. We eat at Tchoup Chop every trip. I would recommend asking for a booth when you call for a reservation. The food is very good. My wife loves the dumplings.
We eat at BICE about 3 times a year because it does have a more formal feel (waiters in tuxes and a piano player) about it. The pasta is made fresh every day. The short rib ravioli is incredible. We have never had anything but good service (ask for Chris to be your waiter). The prices are higher than at Tchoup Chop but to me the ravioli alone is worth it.
I do not think you will be unhappy with whichever you choose. I think it would honestly depend on which you prefer: Italian food or Asian themed food.