The snap traps rarely kill the rodent immediately. Unless the mouse is positioned 'perfectly', then the trap pretty much suffocates them to death or they'll break their own neck struggling to get out. And the squeals aren't pretty.

Sticky traps do just that, stick the animal down to the paper and force it to wait and starve to death [or until you 'take care of it' yourself]. Typically, if left long enough, the mouse will eat at itself in attempt to get free.

C&R traps are really the best. It catches them, you take them out to a dumpster or alley or forest and let it out, you continue with your life and it continues with its own. Never had an issue using them.