The main plus of integrated weights is that you don't have to wear a belt, something which can be difficult for people whose conformation doesn't give them anything on which to HANG a belt
The cons are that a) integrated weight pockets have a limit to how much weight they can carry, and it's a lot less than a belt; b) integrated weights hang all the weight off your shoulders, which can be uncomfortable for some people; c) rigs with the weights installed are difficult to move around on land; d) the location of the weight pockets may or may not be where you need your weight for best balance underwater.
None of these things is a big issue in the tropics, where the total weight required is so small, but they loom much larger in cold water diving.
A final point is that ALL weight systems are trying to accomplish two diametrically opposed things: They are trying to keep the weight you need ON you (losing a significant amount of weight underwater is a very high risk for an uncontrolled ascent) while still making it easy to ditch that weight when it's required. As with octo-holders, weight systems rarely do both well. Velcro, in particular, makes it pretty easy to ditch weight -- but Velcro fatigues and acquires debris, and old Velcro weight pockets are notorious for falling out. I would highly recommend choosing a weight-integration system that uses some kind of positive lock retention mechanism, but even those aren't foolproof.
If you do go with a weight belt, you can either use one of the pocketed belts, like the ones XS Scuba sells, or a belt onto which you install hard weights. If you are going to travel, the pocketed belts are great, because you take your belt, and put as much weight as you need in it when you get where you are going. It's easy to change the weight for different conditions and exposure protection. On the other hand, the pockets on those belts (which are secured with Velcro
) aren't foolproof, so if you are diving at home, setting up a weight belt with installed hard weights is a better strategy. Two tips: One, if you are using a webbing belt, put a metal buckle on it. The plastic ones are NOT reliable. And two, consider one of the rubber free-diving weight belts with a tongued buckle. I was very dubious about this until Dumpster Diver from here on SB just upped and SENT me one, telling me to try it and pay him for it if I liked it. He got paid