Bigger is better but shot placement is King ...
My constant carry gun is a 360PD AirLite with +p .38 loads. At under a pound loaded and holstered it make for effortless carry. Revolver reliability is also a plus with no feeding/ejecting problems.
I also usually carry one of my 3rd gen 9mm as backup for a NY reload if 5 shots is not enough. My 3914DAO is as small and light as many .380's .
I prefer at least .40 S&W if shooting starts and am picking up a 457 in .45 for potential carry.
The .380 "mouse guns" can be effective if the shot placement is well made, but I shoot all of the above with good tactical accuracy so I don't bother with anything under 9mm.