Personally,
I think that there should be no "side of the isle" in congress. The delegations should sit together, like they did in the first few congresses. That's why the senate chamber has pairs of seats, one pair of seats per delegation. If the delegations sat together, there might be a less partisan and more constituent-centric tone about the entire thing.
Well...the Swedish parliament looks like that, grouped after regions rather than parties...it hasn't done much good to the most boring parliament in the democratic world though...