The flow rate of the first stage at depth is the controlling factor in most cases. Most decent quality second stages will perform well at depth, but a pointed out above, the worlds best second stage will not perform well if the first stage cannot supply it with enough air at the full intermediate pressure. Boosting the IP can also boost the airflow of the first stage, so you may want to have your IP checked and possibly adjusted before decidig to upgrade.
I have used the Scubapro Mk 3 and early production Mk 2 and both are fine regs with bullet proof reliability, but can be out breathed when working hard at depth. The Mk 2 Plus has a little higher air flow, but it still would not be my first choice for a deep diving reg. Many tech divers use them on stage bottles, but then He mixes flow through them much easier than air.
A balanced first stage will have a more stable intermediate pressure than an unbalanced first stage. In an unbalanced first stage the high pressure air from the tank presses directly on the HP seat in the first stage and provides some assitance in opening the seat. As tank pressure decreases, so does the amount of assist, and the intermediate pressure consequently falls slightly as tank pressure decreases. With a standard non adjustable downstream second stage, this means the cracking effort will increase slightly as tank pressure falls. In the early days of diving this was useful for "feeling" when your air supply was getting low.
A unbalanced second stage is similar to an unbalanced first stage in that the LP air feeding the second stage presses directly on the seat and provides an assist in opening the seat. If intermediate pressure falls, like it will in an unbalanced first stage, the breathing effort increases slightly.
A balanced second stage uses a balance chamber on the other side of the poppet holding the seat to ensure the force on the seat remains equal regardless of IP. However, this is really not completely balanced as for saftey it must still maintain a downstream design where an overpressure in the LP hose (from a frozen first stage for example) will force the seat open before the max pressure tolerated by the LP hose is exceeeded.
High performance regs tend to also have balanced first stages and in many cases balanced second stages, but balancing in and of itself does not make a reg high performance.