All 1st stage regulators for open circuit scuba use are depth-compensating. That means that they output a specific Intermediate Pressure at the surface, and, as depth increases (which means ambient pressure is increasing), the IP increases by the same amount.
For example: If the 1st IP is 147 psi, that is 10 ATM (atmospheres). That means, at the surface the LP hose to the 2nd stage has 147 psi (10 ATM and 10 ATA) in it. If you then descend to 33' of depth, that means ambient pressure is now 2 ATA (atmospheres absolute). Thus, inside the LP hose from the first stage, the pressure will be 147 psi + another 14.7 psi, or (approximately) 162 psi absolute (AKA 11 ATA) - or still 147 psi above ambient.
Some 1st stages are sold as "over-balanced". That means they are saying as you descend (i.e. as ambient pressure increases), the 1st stage IP output increases by MORE than the increase in ambient pressure.
From the above example, that means that at 33 feet, instead of being 162 psi absolute, it will be something more than that. This is claimed to be a benefit by making the 2nd stage flow even more air the deeper you descend. It is debatable if this is a practical benefit. If your 2nd stage reg is tuned for the absolute best cracking pressure it can handle, then increasing the IP at depth means you are eventually going to make it freeflow.
Many 1st stages are also balanced - like the ScubaPro Mk25. Being balanced is independent of it being "depth compensating".
Some are not balanced - like the ScubaPro Mk2.
For all of them, once the cylinder pressure that is feeding the 1st stage is above some threshold - say, around 200 or 300 psi - then they all will give "almost" constant IP. That is their job.
Being balanced means that the 1st stage will maintain that "constant" IP for longer as the tank gets close to empty. But, again, it only really comes into play when the tank is down geting near empty.
2nd stage regulators also come in balanced and unbalanced varietys.
All the top shelf regulator sets will have a balanced 1st and a balanced 2nd. But, as long as either one is balanced you get almost all the benefit. Having both balanced adds very little improvement in performance over having either one balanced and the other unbalanced.
How much a 1st stage flows it pretty much dependent on the size of the orifice inside the LP port. If you made the orifice really small - like they are inside a HP port - then it would output a fixed IP, but when you inhaled from it, the IP in the LP hose would drop dramatically while the 1st stage tried to catch up.
With a big orifice inside the LP port, more gas can flow and when you inhale the IP will drop much less.
I really do not know if being balanced or unbalanced has anything to do with the size of the orifice inside an LP port. I don't see why it would, but I am not a regulator engineer...
If your purpose is to determine what to buy for yourself, I would expect any namebrand 1st stage on the market to work well enough that, paired with an identical 2nd stage, you would not be able to tell the difference in the different 1st stages. They are all made to be able to flow enough gas for 2 people to breathe off of it and also inflate a wing at the same time. I really doubt one person breathing normally could tell any difference between modern 1st stages.