Snap traps and glue traps are going to be "inhumane" if you care about those things. I've seen a mouse gnaw off its own leg to free itself from a glue trap.
The enclosure traps work pretty well, provided you then have a place to go set the mouse free. It probably would work for someone near rural areas where you can drive 10 minutes, let it go, and not have to worry about it finding its way back. If you're stuck in suburban sprawl it may be harder to find a "naturey" area to set it free. And if you're trapped in an urban environment if you set it free you're just going to create a nuisance for someone else, unfortunately.
The downside to the "no-kill" traps is that they take a little longer to work. If the mouse isn't looking for the food you put in the inside, its not going to go into it. Where as with a glue trap, the mouse accidentally walks on it and eventually it'll die. If you can set up the no-kill traps facing a hole the mouse uses or along a wall where the mouse commonly runs, that usually increases your chances of catching them. Sometimes you just get unlucky and they smarten up and run over or around the no-kill traps.