See, now, I have had recourse to use a chain breaker quite frequently, either for myself or for riding buddies. I find the ones on multi-tools do work most of the time, but man they are not easy and 2 have failed on me. Quite possibly due to user error (how hard can it be!), but both were crank bros and both somehow managed to chew up their own threads.
You can still find each of them somewhere in the forests of the Alsace area, prob a long way from the trails from where they were chucked with great anger.
The one-up breaker works, but man, it is not easy. I had a chain snap last week and it was so humid and wet, my hands were just too sweaty and greasy from the chain to get enough purchase on the stupid tiny chain tool/tire lever that I failed and bodged instread. Have used it successfully when not quite so slippy however.
Thus, FWIW, if you are going to carry one, I recommend to carry a decent one. The mini park tool one is small but it actually works in all conditions.