I have pondered the same question. I own some English side by sides in the weight you talk about. Some are even 2 3/4 chambered.
I would say that the advantage of a 2 3/4 20 gauge over a 2 1/2 12 gauge is cost of shells. The cost for 2 1/2 shells depending on where you buy them can be expensive.
I shoot 2 5/8 Caledonian shells in my English guns and they can be had rather cheaply compare to some others.

Mike Proctor