An unbalanced reg becomes harder to breath as depth increases or tank pressure decreases. It is more a function of the tank pressure as I don't think we could could dive traditionaly deep enough to render the reg unbreathable.
A blanced reg delivers the same ip regardless of depth or tank pressure.Then they shut off
I used unbalanced regs alot in the 70's and 80's. They started pulling hard and we knew it was time to surface. As we surfaced we were able to breath.
Depth compensation has nothing to do with balanced or unbalanced regs; all regs increase the IP as depth increases. This is done exactly the same way in balanced and unbalanced regs, by introducing ambient pressure as a force working against IP in the 1st stage. Otherwise, the reg would not work at any sort of depth.
Balanced 1st stages have greater stability of IP throughout the entire tank range than unbalanced regs...although I have noticed that my balanced MK5 drops a good 7-10 PSI from 3000-500PSI supply pressure and my (unbalanced) MK2 drops about 12-15, so in practicality there's not a huge difference between those two. My guess is that many balanced diaphragm regs in practice do have a slight IP rise throughout the supply pressure range, not that it matters much. In any event, it has nothing to with depth.
One design factor in unbalanced piston regs (the only kind of unbalanced regs on the market) is that the orifice surface area must be kept small to minimize the actual drop in IP by making downstream pressure on the seat a smaller percentage of the total force at work. This limits the practical flow rate, so theoretically if you and a few of your friends were huffing away off the same MK2 at 150 ft, you "might" overbreathe it. The MK2 has a flow rate of almost 100 SCFM, which means it flows faster than the tank valve. If I were a trained tech diver and could do a 200 ft dive, I'd have no problem taking my MK2 that deep.
Balanced 2nd stages use a lighter spring to keep the valve closed and are less reactive to IP changes, so typically a well designed balanced 2nd stage will have lower cracking effort and WOB than an unbalanced. But, in otherwise identical designs, balanced vs unbalanced will result in very little difference.
The terms "balanced" vs "unbalanced" are pretty loaded from a marketing point of view. Who wouldn't prefer "balanced" to "unbalanced" even without knowing what the difference is? Even the PADI OW and AOW books make a stupid reference to it which explains nothing but sends the clear message that "balanced" is better.