I don't think anyone here can comment on which is more "fulfilling" because we're all in surgery because we like surgery. If we liked anesthesia, we'd be doing that. I don't know any surgeons who would consider anesthesia fulfilling or vice versa.
The key point is that, like all specialties, there are also underlying motivations. Very few people approach specialty choice in a vaccuum. To most people, lifestyle is a major consideration. It is to surgeons, too, in terms of worrying about if you'll see your spouse ever or if your kid will know you. However, compared to other specialties, we're much less concerned about lifestyle because we have to be. We know the realities of training.
In contrast, I can't tell you how many anesthesiologists have said to me, "hey, if you can't take the hours of surgery, come join us!" I don't even know what that means. It's like they think that I'll go to a specialty just based on work hours or something. It's the most irrelevant argument ever, but it makes a lot of sense to them. They never say something like, "hey, if you're interested in ANESTHESIA, come join us!" if you know what I'm saying. It would be like if I said, "hey, if you want to wear scrubs, come join us!" to a Psychiatry resident. Huh? What?
If your fiancee is doing surgery right now and likes it, then he likes it. Clearly he knows what the lifestyle entails because he's living it right now. If that's acceptable to him, then I see no problem with it.