The advantage of increasing IP (over the proportiopnal increase in ambient pressure) would be to increase the flow rate of the reg. With air passages of a given area, the higher the air pressure, the more air you can push through those passages (within reasonable limits and subsonic velocities) in a given amount of time. So the idea behind Apek's overbalancing would be to improve the flow rate of the reg at depth. Theoretically this increase in IP will offset the increase in viscosity that occurs at depth where the absolute pressure of the air in the intermediate portions of the reg is higher.
Boosting the intermediate pressure is a lot like turbocharging an engine to improve power output (more mass flow = higher power). However the other approach is to simply use a larger engine with naturally greater mass flow to generate more horsepower in the first place.
What this means in regulator terms is that over balancing really only makes sense in a first stage that is flow challenged already...or as a marketing tool to convince divers to buy your reg as opposed to someone elses.
This also explains why other non "over balanced" regs produce equal or superior WOB compared to "over balanced" Apeks regs. If a reg has decent flow passages and an already excellent flow rate, it does not need to increase the IP at depth to compensate for increased viscosity or inadequate flow paths.
Over balancing also causes a potential tuning problem, especially with non adjustable second stages. The poppet in the second stage is balances the downstream force acting on the poppet with a combination of spring pressure and air pressure from the balance chamber. However, by neccesity the system is not perfectly balanced as you need to have a downstream bias to ensure the second stage can vent any excess pressure that may result from a leaking HP seat that would further increase IP.
What this means is that with a non "over balanced" regulator, I can adjust the cracking effort very precisely at the surface to give minimum inhalation effort at any depth and be assured that this will not result in a free flow at depth. The same is not true with an "over balanced" regulator as I would need to tune it at the surface to have a higher inhalation effort to accommodate the 25 psi increase that would occur at 165'. If I did not, the reg would begin free flowing as you went deeper - exactly what you do not what to have happen. So...with over balancing you may get "lighter" inhalation efforts and lower WOB at depth, but you will be paying for it at shallower depths where you would have higher inhalation effort and higher WOB. An adjustable second stage would however let you adjust the inhalation effort and offset this negative effect.
However a diver is, in my opinion, far better off going with a reg that is balanced to maintain a very precise IP (above ambient pressure) regardless of depth as it will ensure max performance with minimum adjustment regardless of depth.
The term "over balanced" is also a vauge concept. Scubapro, for example, uses the term "over balanced" to refer to the slightly larger diameter of the seating edge on the piston compared to the shaft diameter of the piston. The ensures that the areas of the seating surface itself is totally balances resulting in an extremly stable IP (compare to other "balanced" designs where the actual area of the seating edge itself is often not balanced which can result in a 4-6 psi change in IP as tank pressure varies form 3300 to 300 psi). The term has some meaning and usefulness as Scubapro defines it while the term is basically nothing more than a marketing gimic the way Apeks defines it.