I have used both and there are advantages to both, or not as the case may be.
One thing to keep in mind is how the weight will be handled before and after diving. I have a pouch system (Scuba Pro Knighthawk) with a positive clip, no accidental dump but the quick release is not orange (bad Scuba pro!) and not intuitive. I explain it to my dive buds and make sure they know what's up. Fortunately I have very experienced partners and am very comfortable with them. I am also confident of the system and my comfort with it. I do use my weight belt on occasion.
Have friends who use integrated systems that are not easily removed like mine. A major pain in the ass to lift over the gunnel in rough water. Also a pain in the ass to get to the beach over rocks.
Weight belts work great but I have no butt to keep one up! Also have a friend whose weighs 50#! That's no minor feat to get out of the water either!
In any case, comfortable, easy to use and dependable is what you need.