I'm not entirely sure on the effects of the larger driver for headphones; I know with loudspeakers that larger drivers have trouble producing higher frequencies, but can produce lower frequencies with more pressure as they can displace more air (in other words, a 12" driver is more efficient to reproduce something around 30hz than is a 2" driver - the 12" driver will need much less excursion and therefore input power). With stats everything I've read seems to indicate that bigger is better (as you get more LF extension with essentially no cost aside from power demands), but with headphones that doesn't seem to hold "as much" (in other words, despite the Koss ESP/950 having the largest stat panel in a headphone (if I'm not mistaken; at one point it was), it isn't head and shoulders above anything to come out of STAX (although in reviews between the 950 and the STAX Lambda parts (like the LNS), the 950 is often regarded as having more bass - it is not, however, a "clear cut winner" in all contests)).
When it comes to dynamic drivers, bigger doesn't seem to always mean more bass - Ultrasone headphones use 40mm drivers (I think universally, but I may be wrong), and the experiences I've had with Ultrasones inform that they produce substantially more bass than my Sony F1s (which use "oversized 50mm drivers" (lifted right from the manual)). I've read claims that larger drivers improve sound stage; I'd disagree here too - the Ultrasones were no less deficient, despite again, having smaller drivers (perhaps S-LOGIC influences this, but it still demonstrates that a smaller driver can be made to work). As far as harder to drive, I'd have to disagree as well - my headphones with the "biggest" drivers (53mm) are also the most efficient and can handle the most power (99 dB/mW and 1500mW/ch). This seems to translate with a number of "big driver" headphones aside from my own collection. On the other hand, the most efficient headphones I'm currently aware of (the DT48A.00) use smaller drivers.
Now, to take the above into perspective - the Sony F1s are "full open" and manage bass extension, and I (somewhat, and within context) agree with Sony's claim about the F1s being able to "rival closed headphones" (remember, we're talking about 1998) for overall extension. They use very big drivers, while a number of closed or semi-closed parts (Ultrasone, Bose, Beats) use 40mm (or smaller) drivers and accomplish more bass. The enclosure does matter as well (and other parameters related to the driver aside from size). I've read that the Sony XB1000 (which has 70mm drivers) is supposed to be a monster, but I've never heard one. The reviews that explain the bass are just silly compared to most headphones. That having been said, the "bassiest" headphones I've ever heard used 40mm drivers and were incredibly efficient (and they were headache-inducingly bassy).
In short, I wouldn't put too much worry into the driver diameter or surface area as an indication of quality; it does matter as a spec within the context of the design, but there's other specs that would be needed to get a better bead on what the thing can actually do. Measurement or evaluation of the entire system, once finished, is going to be more relevant (so for example, the Sony F1 has an impedance compensation network in the cups, which likely affects FR, and they have damping material on the back of the transducer housing - so even if you know everything the driver will do in free-space, it's going to change once it's put into the F1 and that is put onto a head; same is true for basically any other headphone I can think of).
