Caveat: I have not read or played Out of the Abyss. I'm going on some hearsay, but generally like what I've heard.
It depends. Do you like Forgotten Realms? If not, go for Princes of the Apocalypse; it's the only one that can be divorced from the setting w/o a ton of work. Tyranny of Dragons is heavily tied to the Sword Coast geography. I gave up on trying to fit it into Eberron. OotA has the Underdark, which might work well in Greyhawk, but nowhere else (AFAIK) has an Underdark heavy with drow (Eberron has Khyber, but the drow are in Xendrik). The map scale for PotA is a bit wonky, but easy enough to drop anywhere and the power groups are easy to file off and replace.
As I indicated, I tried to use ToD, but gave up on it. Aside from being hard to remove from the Realms, it's fairly railroad-y. If your players like to side-trek or push back on being yoked, it's not good for your group. Having read through the module multiple times, during my attempt at converting it, it really makes me dubious of any future work from Kobold Press. A lot of folks have spoken with great respect about the staff. I just don't like the adventure -- even cutting it a lot of slack for being tied to a setting I don't like and being based on a beta version of the rules.
OotA sounds interesting enough for me to be willing to use a setting I dislike (Forgotten Realms), taking place in a sub-setting I dislike even more strongly (the Underdark), with a reasonably heavy focus on a race I despise (the drow). I'm not sure whether the adventure could possibly live up to the hype, but it sounds fun. It also sounds even more difficult to vary than ToD. The play reports, to date, have been mixed, so it probably doesn't live up to the hype. By the time my group is done with PotA, the next adventure is likely to be out, so we'll see what I do.
We're a bit more than 1/3 of the way through PotA, and it's been fun. Yes, there are some issues with the module. Yeah, it's the third dip into the Elemental Evil mega-adventure well. The map scale is really weird. There are sites on the map without entries in the text. And the organizational structure leaves something to be desired (I'd kill for an index and/or cross-reference chart of plot hooks/seeds). Everyone is having fun, though. Life is good. Also, it's easy to go from the Starter Set (Lost Mines of Phandelver) to PotA, which is a plus. It has conversion notes for other settings; these are great for getting thoughts rolling, but clearly weren't written by anyone with a deep knowledge of the settings (at least Eberron). Still a nice warm fuzzy.
Short form: I think Princes of the Apocalypse is the strongest of the bunch. It can be dropped in any setting without much work. It's fun and appears to have the best internal quality, so far.
