It's hard to know what's really going on since there are people on certain online forums that will just plain make up s**t about these clinics unless they are paid a commission. Typically you have to pay a huge markup to get the head surgeon to do the surgery and there are valid concerns about the clinics hotswapping in younger and inexperienced surgeons during the surgery. That's why some clinics even go so far as to use webcams during the surgeries so that relatives or friends can make sure that the surgeon isn't being swapped out.
Wonjin is popular amongst foreigners (mostly Chinese) but I've read some pretty damning stuff about that place (they photoshop their before/after pictures etc). I don't trust online reviews at all when it comes to these South Korean clinics so if you're serious about surgery there then you should try to get in contact with locals there to see what they recommend. The university clinics there is probably your best bet.