To begin, I would say that the most important decision you'll make is the choice of surgeon, rather than the choice of anesthetic option.
For the first eight years I practiced, I did the majority of my gynecomastia procedures in an outpatient setting with tumescent anesthesia and intravenous conscious sedation using Demerol and Versed administered under my direction by a nurse. I did this because I had the facility to do it, and it saved the patients money, since there was a lower hospital cost and no anesthesia fee. My patients did very well, including patients as young as 13 years old.
Since I moved my practice to Boston, I do not have that facility available, so there is no cost benefit to the patients in being awake or asleep. As a result, most of my patients opt to go to sleep. That certainly makes the procedure easier for me, since I don't have to oversee administration of sedation, and I also don't have to worry about patient discomfort during the operation. When the occasional patient requests intravenous conscious sedation (in other words, if he wants to be awake for the surgery), I can oblige him with that, but it's a very different sort of sedation than what I did in the past using more effective and sedating medicines, which are administered by the anesthetist.
You may find that many of the surgeons on this site prefer general anesthesia, since it really allows us to do whatever is necessary to get the best result without worrying about the patient's level of discomfort, and we all have a facility that allows for administration of general anesthesia. Personally, it sounds like your second surgeon is particularly conservative in his approach (a 24 - 48 hour hospital stay is unheard of in the US for this sort of procedure), but if that is his practice, and if he gets good results that way, then so be it. It also sounds like he may be better qualified as a plastic surgeon with board certification in the UK, which is a tough board. Membership in the American Academy of Cosmetic Surgery does not tell me much, other than that the first surgeon has paid dues to be a member of the society.
You may want to check a few more options. At least look at some photos and if possible, speak to a patient or two.
Good luck,
Rick Silverman