You cannot state that routing has a better performance then bridging. It would be akin to saying that taking the plane is better then taking the car. While I would certainly prefer a flight over a drive if I want to travel from New York to LA, I’d much rather take the car to go to my local supermarket.
One bridges traffic in a small local network. If the performance of the network starts to suffer due to an increase of number of clients, you generally subnet the network (making several smaller networks) and route traffic between them. The performance for each new local network will improve but communication between the new local networks will be worse then before. This is because routing is a more expensive operation in terms of processing power.
That being said, routing has several advantages that bridging does not provide like stateful packet filtering, multiple routes to a destination and dynamic routing protocols.
The best solution in your case, based on the amount of information provided, would however be bridging, not routing.