For me, like it looks like it did for most people, it comes down to a comparison between our two favorite lagoon creatures.
I'll start off by saying I went with Crocodile.
Don't get me wrong, I love Doflamingo. He's vicious, highly intelligent, and a bit unhinged. However, from a narrative point of view, Croc benefits from several things that Mingo doesn't.
Crocodile has the huge benefits of being a) the first saga villain ever in One Piece, b) the first major villain in the Grand Line, c) on par (supposedly) with the strongest characters seen at that point, and d) the villain of a very efficient arc.
Doffy has none of those things:
a) That ship has sailed. Croco-boy got dibs and it makes him instantly iconic.
b) Mingo gets to be the first big villain of the New World, but it's not quite the same. The looming build up Crocodile had through Baroque Works is much more subtle for Doflamingo.
c) This is a killer. Crocodile was a Shichibukai like Mihawk, the strongest we'd seen. We've seen Doflamingo wary of the powers of the admirals, Yonkou, and Sakazuki. It's very clear that while he's very strong, he's not even in the top 5 strongest characters, which weakens his presence a bit. The fact that other characters are used to threatens him really costs him some Big Bad points.
d) I love Dressrosa, with all its chaos and complexity, but it's not hard to admit it's very crowded and a bit unwieldy. Alabasta still introduced new characters like Ace, but it was done simply and the plot progressed without enormous detours for secondary characters. The pacing was much better back then, and it allowed for a clearer depiction of the villain.
Crocodile was cut straight from a Bond film, and I love James Bond. Doflamingo has more complexity and character, but I honestly feel that some of the whole "whoooo mysterious background, so dark!" stuff about him got annoying. That being said, those couple of panels in the flashback where he's reading about Flevance and later when he wakes up in cold sweats were brilliant.
Crocodile treats his members just like Blofeld. Mingo is very loyal to his crew but sometimes makes sacrifices. Draw.
Crocodile's character is usually pretty consistent, as he's an arrogant, power-hungry jerk who's slightly amused by the world. His contempt affects everyone equally. Doflamingo, though, bounces between being milliseconds away from straight-up murdering Sanji, the Swirlyhats, and Kyros and savagely beating the tar out of Law to gloating nonstop and toying with Luffy and Law, even going so far as to send clones to taunt them. He says he's getting serious and then immediately goes back to lounging and watching them struggle. It's very aggravating watching him vacillate between hyper-competent and completely cliched.
There are obviously other arguments to be made between the two, but these are the main reasons I didn't pick our brilliant Joker. Had to go with the classic instead.