Its an interesting question, and you got alot of good opinions on it. Since you seem to be talking more about the relatively smaller complications and not life or death, for a routine valve replacement /graft since there are probably about 100,000 valve replacements each year in the US and the success rates are about 98% for everyone combined, my thoughts are there are alot of good surgeons who can do valve replacements/ grafts and after the recovery the vast majority will have a very good life, no matter who their surgeon is or where they went. especially if you are relatively healthy going into an elective surgery. Some surgeons compare their job to that of a plumber once the heart is stopped, changing out bad parts for new improved ones. and as El mentioned chance or luck plays a part, you can go to the best surgeon, and be in great shape, but things can go really wrong, or you might be in rough shape and end up at a place with out as much experience, and do amazing.
Now if you are asking about the rarer more complicated surgeries, like some of the more complex CHDs or multiple REDOS or very sick patients with several other medical problems,emergency surgeries etc., who you chose to let operate can make a bigger difference in the outcome, experience really matters knowing what to do and what NOT to do and not having to stop and think IF something isnt going right, but just automatically go to plan B.
Since you seem to be asking more about the difference in peoples recovery even with very success outcomes, things like different kinds of pain, fever, fluid problems, slower recovery in the beginning, Of course the surgeon plays a part, but the whole team together including the patient, and their experience taking care of heart patients probably makes a differene in all the little things that add up in ways you probably dont even realize
The "best" surgeons tend to (of course NOT always) surround themselves with the best teams and probably dedicated CICUs and "heart floors, so the staff just take care of and become experts in taking care of heart patients and not all kinds of patients so know what to watch for and what to do if something isnt right and hopefully catch it intime before it becomes a larger problem.
Another role the surgeon's experience can make a difference in is surgeons that do these and much more complicated surgeries day in and out, often gain speed so the patients not only might spend less time in the OR, but even more important to recovery, less time on the heart/lung machine which can make a difference in how long or short or complete, your recovery can be.
Besides how young/old, healthy the patient is going into surgery, IMO attitude can make a difference too, believing you will do great and be willing to do everything they tell you to do to the best of your ability as often as you can , unless there are some complications out of your control, usually helps you recovery quicker. If you go into it thinking you will die or have terrible complcations it probably doesnt help.
I think where you have your surgery and their routine probably makes a difference especially in the first week or so in ways you dont even realize or can plan for. for example, many teams believe pain control is one of the most important things they can do to help with recovery. They work with the patient (who this is a time to be honest, if you hurt say so dont act brave or suck it up) to make sure they are in as little "pain" as possible but still mentally with it enough to do all the jobs a patients has to do. Some places will put you on a pain pump in the beginning, or at least give you that option during the pre op testing/talking day and a combo of IV or oral meds.Of course if you ask beore hand they probably will all say they are great with pain control and really dont want you to be in pain, but once you are recoverying you see that might not be true or at least wasn't passed down.
Of course even in the same center "luck" can even come down to who your nurse is each day/shift and their attitudes about pain. Some work hard to make sure you arent in pain andgive you what you need when it is time, others seem to think they are doing you a big favor waiting until you ask for pain meds and not giving them when it is time. Of course than can be a problem since if you wait to be in enough pain to ask for your meds, you are often chasing the pain instead of keeping on top of it. Its good to work with the patient and you dont want to drug them up more than needed, but you shouldnt be made to feel like you are a baby(well wimp not baby since babies seem to have pretty high tolerences for post op pain from our experiences) or junky because you dont want to be in more pain than you need to be.
Then again pain is relative, some people just have high thresholds of "pain" what is really painful to one person another person might not think it was that bad.
Another thing that can make a diffference in the amount of pain you are in, that is different in different centers, can be the choice of chest tubes. There are all different kinds of chest tube systems and beside the number of chest tubes you start out with, what kind they use can make a difference in how painful they can be. Some places use the large stiff chest tubes hooked up to the large box with chambers and water, usually sitting on the floor, other use much thinner softer tubes that can be hooked up to a little bulb and all kinds in between. Not only can the larger tougher tubes cause more pain inside banging around, especially when you are moving around or walking and when they come out, so could cause more irritation than softer smaller tubes. Would it make enough difference or even cause more fluid to build from the irritation? I dont know but I would think it could in people who tend to, but it can make it a bigger project just to get up and do your laps, especillay if you are hooked up to IV's catheters oxygen etc, its one more big thing to lug around. Of course there are sometimes you can't use the smaller systems, if you can it can probably make the recovery easier.
Another pain some people have is stomach pain, often caused or made worse at aleast by pain meds. Some places are mcuh better at keeping an eye on that, giving some kind of fiber before it becomes a problem. Others wait until the person is constipated and in pain then try to help it.
One of the other things that can be different between doctors/centers is meds. Some places automatically give certain meds to most heart patients, just "incase", while others only give them IF they have to, like a Amiodarone that has ALOT of bad side effects and even the manufacturer says to give as a last resort IF a peson is in Afib and other meds didnt work. Some surgeons/centers treat it like it is as safe as tylenol. There are other drugs that come with nasty side effects that maybe if a person chose a different surgeon/center they might not have even been put on, so wouldnt have that side effect and need more drugs to take care of those side effects.
So I guess my answer would be the surgeons skill plays some parts, the rest of the staff and what is normal procedure probably plays a large part part of this beside things i gave examples of sometimes its a matter of is even tho they might seem mean or pushing to to hard, some places /nurses really keep on you to get out of bed early, make sure you are doing all your walking and breathing exercises etc IF you aren't motivating yourself, others might wait a day or so to have you walking around etc.and of course the patient plays a part, not only in choosing when and where to have surgery and working as hard as they can, but perception can make a difference, There are people who most people would think they had an AWFUL time, run into all kinds of complications, need more surgeries etc, but if you asked they say it wasnt too bad and then others to the outside world looks like they really were lucky as far as size and number of incisions, recovery, complications, but to them it was the worse experience possible and they think they had it terrible. Some people also can worrry more than others so focus on every little thing and stress themselves out so the whole experience was bad with all kinds of complications in their mind, which is really all that mattters, when others seem to go with the flow more and even if they have a bad bump or too, looking back even a month later thought since they were home in roughly the average time and feel pretty good, they had a good surgery and recovery.
So I probably made this even more confusing than when you asked