This sounds like it was not the fault of your BC (unless it was leaking), but just a lack of experience on your part. You might have also been overweighted, causing you to need more air in the BC, which makes it more sensitive to depth changes. You should consider finding an excellent technical diving instructor or recreational instructor that does some technical diving, and ask him or her to help you with your buoyancy. It would be best to do this in a BP/W so you can try one out, but even with a jacket BC it might be very helpful. There's a buoyancy class offered by most of the agencies, like PADI's peak performance buoyancy. With the right instructor that class can be very helpful to new divers.
Trim in the water is primarily a function of weight distribution; the typical problem is that many new divers are overweighted and too much of the weight is down around the hips. Combined with an aluminum tank this can cause new divers to have trouble staying horizontal. The BP/W puts some weight up on your back and helps distribute it more evenly. You can do something similar with almost any BC, by putting weights on the cambands with little pockets that are made specifically for that.
Two of the biggest advantages IMO of the BP/W are that it holds the tank in a very stable manner on your back and that there is very little clutter and extra material/padding/buckles/kitchen sink in front of you in the chest and abdomen area.
I'm not a fan of integrated weights, but it really depends on how much weight is involved, what type of pockets they are, what kind of tank, etc. The whole issue of weighting/trim needs to be considered with all the factors for an individual diver to come up with the best solution.
where i live i dive 1 mm wetsuit. i bought Mares 5.4.3 wetsuit based on the company recommendations. didn't do any dive with the Mares suit before the liveaboard.
im 85 kg. use 5-6 kg with 1 mm. so the instructor on the liveaboard told me i have to put 12 kg for the 5mm.
after first dive, i removed 4 kg, did a weight check but i was unable to descend, no matter what i do. i put back 3 kg and also was unable to desend unless i desend top down and kick untill im at depth of 3-5 m then im good.
had to dp negative entry on all the dives after that. bottom line, once im at depth of 25-30 m, the BC wasn't helping me.
after one of the dives, i removed my BCD, kept my mares wetsuit on and since i like to freedive, i decided to jump on the water, what i found out is that the model i have act similar to the life guard jacket !! kept me floating.
i often read on different threads that someone want to buy a regulator, fin or a BCD and soooo on, then he says something like, i will go and try it out with my LDC. here, there is no options, for example, aqua lung dealer only have Wave BCD for rental, and i can't remember the regulator name but its one of those bottom end regulators, asking a trial of axiom or black ice or xtx100 is not possiable. that is just an example, other dealers like oceanic and scuba pro is the same.