I haven't read all the responses, so I apologize if this is redundant. There is a big philisophical difference between diving doubles and diving a single with a pony.
Think of each setup in it's three components:
1. gas supply for the dive
2. gas supply for emergency
3. safety control
Most successful divers have a gas plan. They know based on a predetermined profile, how much gas they will need to complete the dive surface to surface, while maintaining some sort of reserve for emergency contention. To take that even further, they may have considered what if my buddy needs gas at the worst possible time as well. I won't go into the different methods of planning other than that they exist and drive how much gas you would need for a given dive.
Most people would agree that dives shallower than 60 feet don't 'really' require added thought in regards to redundancy or extra safety gear. A CESA (controlled emergency swimming ascent) should be able to be performed from this depth in the event of equipment failure. When you start approaching 100 fsw, the amount of time, and therefore contingency time, gets small on an AL80. As you dip below 80 fsw and push the RDP, many divers start looking at larger singles to provide adequate bottom time. So how does this break down into doubles vs single with pony?
Some portion of the gas contained in a set of doubles is off limits. It is held in contingency reserve, and for the sake of argument, it is equal to 33% of total gas. That leaves 66% of the total content to be used for total runtime. That 33% is for accidental bottom time overruns, or in the worst case, getting a buddy back to the surface from the furthest point of the dive.
The same holds true for a single with pony. Typically, the pony is off limits, except in an emergency, so the single is used for runtime planning. The pony should be of sufficient volume to perform the same function as the 33% of the doubles volume, based on planning for the same dive.
Example:
Double AL80's give 160 cf of total gas, 106 cf of dive gas, and 53 cf of contingency gas.
A single HP100 mated with a 40 cf pony yields approximately 140 cf of total gas, 90 cf of dive gas, and 50 cf of contingency gas. (Notice, we don't breathe the single down to a vacuum unless there is a need)
These two setups give very similiar yields in planning a dive to the same depth. You can play with different tank sizes to get different compatible configurations. An AL40 used as a pony would normally be slung under the arm vs attached to the backgas. The thing to note here is that for the same dive, most single tank divers would probably not be taking enough contingency gas, as mounting AL20/30's to a large single is the facto standard. This is one reason why I am not a fan of this configuration, as most divers don't really do the calculation.
Now, with apples to apples on the dive plan that would require 90cf of gas (so either double 80's or a single 100 with 40 slung under the arm), we start to take a look at the safety controls. The doubles have two tanks, two tank valves, an isolation manifold, and two 1st stages. The single with pony has two already isolated (no manifold neccessary) tanks, two tank valves, and two 1st stages. The completely independant tanks do not require the isolation manifold that the doubles do.
In the doubles configuration, all gas is available to the diver without the need to switch regulators or turn on tank valves. The isolation valve and two tank valves are open prior to and during the dive. They manage one spg and know at any given time the status of supply.
In the single with poiny configuration, only the dive gas is available to the diver. If contingency gas is needed, the diver must open the pony valve (if not dived in the open position) and swap regulators. Not a big feat, but an extra step while possibly gagging for gas if the planned bottom gas is expired.
Failures or leaks in the doubles can be isolated to where 1/2 the remaining gas at time of failure can be saved. At the furthest point in the dive, which would be at 33% of gas consumed, a failure would leave 50% of the remaining gas, or 33% available for getting home. A failure or leak on a single would require a bailout to the pony, and all bottom gas would be lost. At the furthest point in the dive, which would be at 50% of the 90cf plan, a failure would leave the diver the pony to get home. This failure on this setup may leave the diver with just shy of adequate gas to get home.
Leaks are one thing, because leaking gas still leaves gas to be breathed until it is gone. On doubles, one would breath down the now isolated leaking supply, and then switch to the other regulator and tank. On a single, the diver could breath down the leaking backgas until empty, and then switch to the pony. This type of failure isn't as critical as a catastrophic equipment failure that leaves no gas in the supply cylinder. This is where the doubles have the advantage over the single with pony (see example in preceeding paragraph). To make diving a single more fault tolerant, one can add an H-valve, which mimicks the isolation valve on the doubles. An h-valve puts a second regulator on the single tank with the ability to isolate either regulator. A valve or regulator failure with an h-valve would allow you stop a catastophic gas loss via isolation. The one single tank failure that is not serviceable underwater is a blown o-ring on the tank neck. The diver is forced off the back gas and on to the pony when the gas is gone (usually very quickly).
So, the gear is kind of different, but kind of similiar. The safety controls can kind of be the same, but kind of different. The doubles allows a simpler setup for an apples to apples dive without the need for a large slung or mounted pony. The single/pony setup loses it's ability to mimick the double configuration when anything over double 80's or a single 100/40 pony is needed. The size of the single starts getting huge and unmaneable for most above a steel 108, because the size of the pony needed goes above 40 cf.
For shallow dives where an AL80 with small AL30 can be used appropriately, doubles would be too much. But at the depths we're talking here, a pony isn't really much more than a spare air. Proper gear maintenance and proper buddy protocol should alleviate the need for a pony at these depths. This would leave solo diving in the 60 to 100 fsw as the only instance where I would consider using an 80/30 combination. Beyond 100, I'd go to double 80's, and shallower than 60, I'd do a CESA and leave the extra gear at home.
I hope this wasn't too conveluded, and I hope it helps some. There is more detail behind these practices, and I'm not trying to train anyone here, so please take it as advisory based on my practice in the past before I went over to a reabreather.