When I talk to others about what they are flying, I sometimes get the remark that "A higher voltage battery (such as 4Cell vs 3Cell) results in longer flying time.

That is not always true.

It is probably true that if you take your quad that is now flying on a 2700mAH 3Cell battery, and replace it with a 2700mAH 4Cell battery, you will get a bit more airtime. But the difference is not because the battery has a higher voltage. It is because a 4Cell 2700mAH battery has 33% more stored energy than the the 3Cell 2700mAH battery. But both are rated the same - 2700mAH.

In order to get true battery capacity you have to multiply the voltage by the mAH rating. It takes 1000 milli-Amp Hours to give one Amp Hour (since there are 1000 milliamps in one amp). A Watt-hour is a measurement of energy, so I like to use WATT-HOURS to measure the capacity of the batteries I use. A 4 Cell battery produces about 16V, so the 2700mAH 4-cell battery holds (2700/1000) * 16 = 43.2 Watt-Hours, while a 2700mAH 3-Cell battery has a capacity of 32.4 Watt-Hours.

A 2000 mAH 4 cell battery has almost exactly the same energy storage capacity as a 2700 mAH 3 cell battery.

It IS true that to produce a given amount of power, the current in Amps is lower for a battery with a higher voltage. That is true. Lower currents result in lower voltage losses in wiring (assuming that the wire sizes are the same), so it is possible that there will be less system loss if a higher voltage battery is used, but again, that isn't always the case. ESCs have losses as well, and depending on the design, those losses may be lower or higher at higher voltages. Lower because of lower currents, higher because of higher switching losses.

I have generally found that - unless you are drawing more than 60A from your battery, you should try to use 3 or 4 cell batteries. If your current demands are greater than that, or if you wire runs are very long, then you should use a 5 or 6 cell arrangement.

Of course, choosing the cell count depends heavily on the prop size, the KV rating of the motor and the motor maximum current, but if you are designing "from scratch" and have total control of the system, I would start with a 3 or 4 cell setup and work from there.

Also note that many ESCs are not designed to work with more than 3 or 4 cells. You may be able to violate that spec for awhile, but if you do, you will have an unreliable piece of hardware in the air above your head.