As much as I love knives, I'd probably choose a multi tool if I had to pick one or the other as my only knife/tool. They're just too handy. Everytime I leave my house without my Leatherman, I regret it.
I just got back from a three day camping trip. My multitool was used numerous times everyday. Opened soup cans (we forgot to bring a can opener), used the pliers to removes painful burrs from clothing and shoe laces, used the pliers to grab hot items off of the fire, used the saw and knife to make impromtu clothes pins to hang wet clothing, etc. I even hastily made this fire grate:
It's also nice to have a pair of pliers while fishing for hook removal.
I've also done numerous small home repairs with my multitool and never had to run out to my shop to get tools.
When I worked in road maintenance and grounds maintenance, my multitool was indespensable. I now work in an office and don't use it nearly as often, however it still comes in handy in an office setting. Additionally, it's just nice knowing I'm a bit more prepared.
All this to say, multitools are a compromise in many ways, but I find them extremely useful. Your milage may vary...