Oh gosh, this is getting geeky, isn't it!!
Very briefly: Important to distinguish between the 2 different types of compressor surge - on boost surge, and off boost surge. Ginger Prince (Mike) above has off boost surge, where the throttle plate is snapped shut and the turbocharged air in the compressor has no where to go except to the diverter valve, and if this isn't up to the job, will surge the compressor. On boost surge is where you get compressor surge because the compressor stage is trying to shove more air into the engine (throttle plate open), but the engine can't ingest this volume at these revs, so the turbo is operating to the left of the "surge line" on the compressor map. In this instance, a ported shroud can alleviate compressor surge, as it is effectively widening the surge line of the compressor, by "bypassing" or "leaking" some of the unwanted charge. So a ported shroud is only of value if you suffer from these specific circumstances.
Bigger turbo & higher flow rates at lower rpm - I'd have to study the compressor maps to definitely answer the question, but briefly - in a steady state condition (fixed rpm) yes, a larger turbo can yield a higher flow rate compared to a smaller turbo, however, in a non steady-state condition (like in a car), other factors come into play that may outweigh that advantage (such as longer spool times, increased inertia, the efficiency line with respect to rpm will change etc.) So we start getting into twin-turbos, and quad-turbos to overcome these issues
But one of the most important factors is the overall gas flow velocity throughput - much like boy racers that put on 4" exhaust pipes in the belief that this will improve the breathing of their car - quite the opposite, because of the larger diameter, in most cases, they will have reduced the overall gas flow velocity, and set up all sorts of problems with engine breathing (urban myth = exhaust backpressure is good).
/geek