This is of course only one piece of data, but I tried Ubuntu and Mint both, and Mint just worked, and Ubuntu didn't. Most things worked ok in Ubunta, but I have one program I use (and won't give up) that Mint just runs, no problems, that sends Ubuntu off in the weeds. I think it is something about my system that is likely the problem, so my experience may not at all apply to you. The bottom line, though, Mint works, Ubuntu doesn't (and I read the Ubuntu forums, and at least two forums associated with the program, and posted asking for advice several places, never was able to make it work). I really get the impression that Mint goes somewhat farther in providing a great out-of-the-box experience.
Also, like some of the others said, I really just find the Mint experience more open, less, I dunno, corporate, maybe? Obviously, if you come to the Mint Forums, you are likely to find a lot of people who prefer Mint, or we wouldn't be here.
Really, though this probably doesn't help, probably the best way to know is direct experience: Install distros that appeal to you, use each of them a few days, try to make them work with what you need to do, and see how things sort out. That is one of the many things I love about Linux! There are lots of distros available, and they are completely free to try (other than your time).
Good luck exploring Linux!