No question here: Integrated all the way! Only time I've used weight belts is the first pool session in class a long time ago and if I dive without my own gear. I HATE a belt now.
I have an old Zeagle BC that just uses zippered pockets for storing the weights with a rip-cord that unlaces the bottom of the pockets for dumping the weight, so there is never a problem with unexpected dumping.
Only time a belt sounds good is in a small boat when you have to hand up your equipment before getting out of the water. It's easier to hand up the belt, then your bc/cylinder than the whole thing loaded up.
Any other time, it is just as easy to carry the weight separate from the bc until you are ready to jump in the water as it is to carry a weight belt. If the bc weighs too much loaded up for carrying, assembling, or whatever, take the weight out. (I carry my bc on my back weighted up and also carry my wife's weight in my hands to take some strain off of her.)
Bottomrunner: When I have to take my bc off under water, (only in class or practicing), don't let go of the bc. I usually use a 1mm suit, so I only carry 8lbs in salt, but at 15', we'd go in opposite directions. At about 40' or so, I can be neutral or negative without the weight by adjusting my breathing, so no problem here.