Monopods and tripods are both compositional tools, but only the tripod allows long exposures. The cost is that for the added capability, a tripod is bulkier, heavier, slower and more complex to use. They're also more expensive, and more likely to get you into trouble with photographer-phobic Authority.
It all depends on what your goals are and your tolerance for hassles, both logistical and interpersonal.
My usual solution is to get one of everything.
A Slik Compact tripod costs slightly more than nothing, folds up small enough to fit
inside a decent backpack, and is still tall enough to be useful. Compared to my Seven Pound Monster, a Gitzo Explorer with a Manfrotto junior geared head, it's flimsy and a pain to use, but it's also one that I'll carry when I may not need it and it gets the job done.
With the money you save on the tripod, you can now afford a decent monopod with a ball head.
I have two monopods; a heavy Manfrotto three-section one with a ball head, and a lightweight 4-section Manfrotto "Digi" fitted with a swivel head. (Both have QR plates.) The Digi is good for casual use, and I keep it at work so that I can take it with me on my lunch-hour stroll. It's still a little flimsy, but it's light and small, and gets the job done. The bigger monopod keeps my seven-pound monster tripod company in the closet.
Swivel or simple ball heads are very important with a monopod -- they allow you to hold the monopod braced against your leg or another object, and greatly increase your stability. A decent link is
here. Another advantage of the swivel or ball head is that instead of detaching it via the QR plate and having two things to carry, I frequently just collapse the staff and lock the swivel at an acute angle. This lets me continue to stabilize the camera with the `pod over my left elbow or shoulder. Even when the swivel is locked vertically but not touching the ground, the added moment of inertia will help me keep the camera steady.