I have a fullsize .45 and a 10mm Glock, and I carry a G29 or G27. I load for all of them.
The 10mm can fire bullets that have a higher BC, greater sectional density, and they can be driven pretty fast. The 180's and below are pretty fast, and 200 grain bullets can be supersonic or subsonic. Because of this, the round shoots flat and is pretty accurate at distance, and retains more energy. I love shooting it.
The 10mm can simply deliver more energy to the target than the .45 can, provided the round doesn't overpenetrate, which could be easy to do with a 10mm. A clogged XTP (can't recall the weight) will go almost 3 feet in gelatin. You also have 15 rounds in a G20, or 10 in a G29, which is nice. When loaded for defense, I mostly use fairly warm 180 grain loads, but always within published data. I don't load "hot" rounds. They are more powerful than the .40, but they have less recoil due to the larger and heavier pistol. Typically, the 10mm has about a 300fps advantage over the .40.
As far as defense though, that happens at close range, and a .45 will do just fine. I like the 10mm because of the accuracy, capacity, and because I like shooting it. I figure the last is more important, since I will shoot a lot on the range and probably (hopefully) never at a person. So either will work for that, but I think the 10mm is more fun to shoot.
If you don't handload though, just stick with .40, or better, .45. Factory 10mm ammo is watered down quite a bit, and the only thing you gain is reduced recoil. If you do handload, don't overdo it either, 10mm is forgiving, but not supernatural.