Why lug a toolbox around with you when you can have a toolbox that fits in your pocket or on a belt?
I d never suggest that a multitool can take over the job of a proper toolkit, but a proper toolkit is only any good to you if you have it with you.
There are countless multitools on the market, ranging wildly in terms of price, quality, and features. Since I live by the adage of buy cheap, by twice I prefer to pay a little more and get a quality item. This is why I always carry a Leatherman tool with me. The company offers over 30 to choose from. I like my multitool to have a pair of solid pliers, decent screwdrivers, and a pair of scissors.