I sure hope your "local constabulary" doesn't carry #6 shot in their duty shotguns...

Look, heed what others have already mentioned. Birdshot is NOT for dangerous home invaders who will we close and who might be heavily drugged or enraged. Just NO.

I use #1 BUCKshot for HD work. 16 pellets of .30 cal round balls at 1250 feet per second. Penetrates a bit less than 00 buck, but much larger overall permanent cavity damage.

I do not recommend mini shells for defense work. They require adapters to feed properly in most shotguns and your first shot effectiveness (you may only get one shot off) is notably reduced. They are largely a gimic for our purposes.