Given that a gun is hand held and the birds are flying targets, no shotgun and shooter combination I've seen in action by any hunter I've run across in the field is consistant enough to guarantee a clean kill every time. Your mileage may vary.

The 12g shotgun probably wounds more game every year than all the other gauges combined.

A .410 puts out plenty of shot to kill a ole cock bird daed. Yes, D-A-E-D. 'pends on how far and where the pattern was relative to the ole cock and how big the shot is. Maybe you just need shootin lessons from a good instructor? I know a good one.