As you can see from the answers here, some surgeons prefer each technique, and it is certainly true that either technique can produce a good result and a satisfied patient. However, there are some important differences, and you are wise to look into the options.
I certainly agree that a surgeon's experience with each procedure is important. The "trimming" procedure is technically simpler, and less likely to cause complications and problems during surgery, as long as we stay away from the clitoris, which is anatomically at the front of the labia where they come together. However, trimming alone will not reduce the fullness in the clitoral hood, so if that is important to you, be sure that the surgeon plans to address it.
I do not agree that the wedge procedure only improves the central portion of the labia. By taking out a wedge, the tissue in front is pulled backward and the tissue in back is pulled forward, and that does reduce the excess tissue in those areas as well.
Also, with the wedge procedure, we can extend the outer limb of the wedge toward the front, on either side of the clitoral head, and get some good tightening of the excess tissue over the clitoris without making an incision directly over the clitoris (which might endanger that very delicate anatomy)
Because the wedge tightens the entire length of the labia, it can improve the area around the clitoris as well. With the trim method, the surgeon has to stay about 1 cm from the clitoris, which means that you may be left with a boxy "tab" adjacent to the clitoris where the labia could not be treated.
With the inner limb of the wedge (that goes toward the opening of the vagina), the surgeon should be certain to stay away from the opening of the urethra (where your urine comes out). I often put a catheter into the urethra at the beginning of surgery to make it easier to keep track of the urethra and ensure that the opening is not damaged during the surgery. The catheter is removed at the end of the procedure.
I have not seen significant healing problems with either technique (and I have done both, although currently I mostly do the wedge resection). As with any surgery, minor problems might require a revision.
I would agree that, for very long and large labia, trimming might allow us to remove more tissue, but in my experience, a very significant amount of reduction can be done with the wedge procedure.
So, I would compare the techniques like this:
Does not disrupt or remove the delicate free margin of the labia minora
Tightens the entire length of the labia minora, including the portion next to the clitoris
Can be carried forward on either side of the clitoris, tightening the clitoral hood
More complex procedure, requiring more skill, to reduce the chance of too much tightening of the opening of the vagina or injury to the urethral opening.
DOES remove the delicate free margin of the labia minora, which might be an advantage for a patient who does not like that pigmented tissue and wants it removed
Removes tissue along the entire length of the labia minora, except for the area immediately next to the clitoris, which may produce an extra "tab" of tissue there
Does not improve or tighten the clitoral hood. If this is important, the trim can be combined with another procedure to reduce the clitoral hood, with an incision that may or may not be directly over the clitoris
May be more effective for very long and enlarged labia
Simpler and less technically demanding procedure
The only absolute rule I would suggest is that you NOT try to talk a surgeon into doing a procedure with which he or she is not completely comfortable.
However, the good news is that labiaplasty is a great procedure for improving both the appearance and discomfort from enlarged labia.