The difference between the UK and US is that, since you pay up front in the US, you get some more choice. Different surgeons will seek to promote themselves to get your business.
In the UK, with the NHS, treatment is free at the point of use. You are allocated a surgeon, capable of doing the relevant work, who is available.
While the individial skills of different surgeons will vary, generally, surgeons are all very highly trained and very professional. Any surgeon is unlikely to risk his entire professional reputation by taking on something that he doesn't have the skills for, botching the procedure.
Individual patients vary enormously. Each body tends to react differently to trauma. The mental/emotional attitude of patients plays a very important part in recovery as does the individual physical health.
But if you can afford it, then, by all means, go overseas.