Depending how you designed the rules, The house could move faster than the Senate. This is certainly possible under the People's House envisoned in the Duke Plan.
As I would see it, the House would pass stuff quicker and the Senate would be the ones to sift through and improve that at about the current pace. And you could have a fast track for emergency stuff with both houses proceeding simultaneously.
Generally speaking though, concerns about effficiency have always been what has hindered a bicameral system in this game. I think those problems could be overcome. When polled in 2013, Duke's proposal (for just the bicameralism portion) had plurality support. It seems opinion has shifted negatively since then.
I think that's also a better idea.