The Apeks "overbalanced" myth is getting a little old. This myth basically states that the IP increases more than the ambient pressure as depoth increases meaning the difference betwene IP and ambient pressure becomes larger at depth.
I have never seen any evidence of that in working on the designs. To be honest, it would not be a good thing as it would 1. ensure that the reg would eventually freeflow when the depth is deep enough and 2. require the second stage to be detuned to ever greater amounts resist that effect at ever deeper depths.
I'd like to point out that the technical descriptions you provided links to are at least accurate and clearly state that the intermediate pressue will remain a CONSTANT 9.5 bar above ambient regardless of depth.
However, that is ALSO true of an unbalanced Mk 2 Plus, not to mention any other unbalanced piston, balanced piston or balanced diaphragm design and has nothing to do with what is considered to be "balancing" a regulator. ALL scuba regulators incorporate a means to increase the intermediate pressure by an amount equal to the increase in water pressure at depth to maintain the differnetial between IP and ambient pressure.
What "balanced" regulators do is incorporate features that balance the area of the seat (piston first stage) or seat carrier (diaphragm first stage) affected by the upstream (diaphragm first stages) or downstream force (piston first stages) of the gas flowing from the tank. This means that in a balanced first stage, the IP does not increase (diaphragm first stage) or decrease (piston first stage) as the tank pressure drops. That allows the second stage to be much more finely tuned and to generally offer a lower inhalation effort.
In terms of flow rate, an unbalanced regulator IS limited in terms of the size of the orifice that can be used. A larger orifice means a greater change in up or downstream force which in turn means greater IP change - unless a larger piston head or diaphgragm diameter is used in the design, and practical size and weight limits quickly place finite limits on that dimension. So unbalanced piston first stages tend to have low to medium performance levels. BUT on the plus side, they have only 1 moving part, only 2 dynamic o-rings and no high pressure dynamic o-rings, making them extrmely simple and bullet proof designs. I prefer them on my deco tanks as they need to work no matter what.
In general, the flow path of a "flow thru" balanced piston design like the Scubapro Mk 25, allows for more brute performance and gas flow. However a good balanced piston design like the Scubapro Mk 17 or Aqualung Legend offers more than enough performance for any rec, deep air or mixed gas technical purpose.