Hands down it would be the PCT as my favorite, and this isn't just a matter of "be true to your school" (I live in WA state, the PCT is sort of my 'local' trail). The PCT is for me (and I think many/most I've talked to) the best balance of beauty, scenery, and variety of terrain and experience, balanced against the 'cost' of hiking it, i.e. it didn't kick my butt too-o hard. The CDT is the toughest of the trails (though I think I started a bit too early on a fairly tough year), and the AT is IMO just about equally tough as the PCT, but with less (or at least different) benefits.

ONE word for each? That's tough. Can I have two each??
AT: "Least Scenic"
PCT: "Beautiful & Varied"
CDT: "Beautiful & Tough"

Okay, and I'm cheating with the ampersands, but ... !

I don't mean to completely knock the AT; living on the west coast, it was kind of cool from a history and geography perspective, and really a cultural perspective to hike that trail. I'm not saying it has no scenery (!), just that the knock about it being a 'green tunnel' is indeed more true than on the other two trails. And unlike what some folks think, the AT isn't necessarily easier; it's "differently hard". The Whites and parts of Maine can be quite difficult, and the "pointless ups and downs" and the overall trail quality (despite a lot of work by dedicated trail clubs) is lower. And also on that trail, I started on the early side (late Feb last year) in a high snow year for the south, which likely skews my sense of how difficult it is vs. the others (the coldest nights I had on any of the trails were down into the teens on the AT in Georgia and Tennessee/North Carolina).

There are of course great benefits on the AT too: generally the least amount of food, water, and gear to carry makes for light pack weight. Great and frequent trail towns and associated trail culture, where the thru-hiking phenomenon is well understood along the way. But my personal opinion is that the AT is so popular only due to inertia and the relative populations --- so many people live in the eastern part of the country and naturally want to hike "their" long trail. IMO would-be thru-hikers would do better to make the PCT their first long trail attempt if they think it at all likely that they'll only do one thru-hike. Unless due to proximity or for whatever reason, the AT is just more 'meaningful' for you. In which case, of course, hike the AT !

But I have little incentive to walk much of the AT again. Parts of the CDT I would like to see another time, in somewhat more benign weather conditions. If I were do to any significant miles on any of these again, however, it would definitely be the PCT.