To be honest, not a question I'd thought about much before, but I'll have a shot at it - call it my take on the concept.
Surgery was generally avoided whenever possible. That gave infections a good shot at killing you, and from what I've read in a number of history texts, even minor injuries could lead to some pretty severe consequences. Surgery, sadly, tended to kill more people than it saved, and those it didn't kill sometimes wished they had died. Cauterization of wounds was common, which would ensure no healing would take place thereafter. Amputation was commonly used as a last resort (outside armies in a war, where it was used considerably sooner than that) which meant that gangrene could take hold, and by the time the victim finally plucked up enough courage for amputation, it was often too late. Remember, with a limb missing, you couldn't work in most jobs, which left relying on family or begging as options. So, surgery was a last option.
Because surgeons were prohibited, in most cultures, from cutting up bodies, living or dead. (For religious reasons, by and large) That meant that they were often working blind, so to speak. Add that to the fact that a successful surgeon often had little or no knowledge of (or interest in) hygiene and some wore their blood-soaked aprons to advertise their experience, and you can start to see why they were often referred to as butchers (and that pejorative is still used even today).
If you wanted to find a surgeon who had some clues, you'd ask around to see who had the most surviving patients. Alternatively, and this was a good way for a character wanting to gain surgical experience, follow an army around. The surgeons there had a lot of experience in stopping bleeding, dealing with infection, and amputations. They may have erred on the side of safety, and performed amputation a little on the early side, but they had a lot of experience with what an untreated infection could do. As a character, you'd have a chance to explore anatomy that way, though unnecessary experimentation could lead to an early death at the hands of the friends of the dead, friends who were very handy with weapons.
Now, if you wanted to go for herbal cures, there were a number of options. Apothecaries existed who could provide you with what were believed to be efficacious cures for any number of conditions, and often were effective, although sometimes the side-effects were somewhat less appealing. Herbalists existed, and wise-women were often consulted (usually by women rather than men) about herbs that could cure any number of problems, especially ones that people tend not to talk about. This could easily be a character option, especially as it would encourage them to explore strange places, and search for knowledge.
So, slow healing via herbs (though faster than without them) and reduced infection chances, but with a number of side-effects.
Fast healing via surgery (though with a risk, or certainty, of permanent damage) and ways to stop things that herbs can't touch (bleeding and such) but with increased chances of infection or the chance to append the nickname "Peg-leg" or "One-hand" to your name.
And wonderful role-playing options open up for characters who want to go into medicine. Searching for new herbs or combinations of herbs, old recipes for healing salves and potions, hunting down a healer who is rumored to have found a way to cure disease X, finding the missing ingredient for the salve you want to make, which can only be compounded while fresh -all good for herbalist types. Then there's the forbidden anatomy practice, grave-robbing to find appropriate bodies to experiment on, and the ever-present danger of the law/necromancers/other surgeons while doing so, escaping the vengeance of the family whose beloved father died on the operating table... ain't the life of a surgeon wonderful!