I've only played two, Bull and Solas, both with male Lavellans.
Not surprisingly, Solas wins out as the best simply because it is so tied into the plot, and the relationship actually revolves around your character's race and heritage, which hasn't been done before. The fact that it ends fairly tragically also makes it quite moving. Each of the romance scenes (there are three) advance the relationship in a meaningful way, and also shed light on Solas's character and personality and even motivations (his reluctance to continue the relationship each time, for instance... you later learn the reasons behind that reluctance). The flirts are quite natural, not raunchy at all, and excellently voiced by both parties (though I can't speak for anything but the male English inquisitor voice). What was kind of funny to me was that my inquisitor sounded rather flirtatious while Solas just seemed a wee bit flustered. Though when I flirted with him as a mage, his personality changed ever so slightly; he was more aggressive then. Very interesting.
Bull's was not a bad romance (even if personally it was not great for me at all); it had a lot of scenes and explored something that hadn't been explored before in the games (BDSM). His character however isn't as integral to the plot as Solas', and there really is very little tension in the relationship, so it simply doesn't have the amount of drama that Solas' has. The ending can be potentially tragic, but I wish that tragedy had been handled better. On top of that, I don't think FPJ's voice was consistent enough for the character, and that hurt quite a few scenes and took me out of the story a few times.
The only other romance I will likely play is Cullen's (again with a male Lavellan because I am boring like that); I'm guessing it'll be in between the two, simply because the Cullen romance allegedly has a LOT of scenes; also I think the voice actor really stepped up his game, so I imagine that adds a touch of subtly to each romance scene. Unfortunately the character seems a lot more vanilla than in the previous two games; there's no longer much controversy surrounding Cullen, and thus I think his romance could end up being, well, again, vanilla. Perhaps a little too romance novel like.
As for the others... I might consider romancing Cassandra with a mod (female, not sure what race) but it seems unlikely just because I can't imagine my playing this game four times, ugh >.<
I started the Blackwall romance but the two were confessing their feelings for each other during the first scene in Skyhold, which took me by complete surprise because all I recall doing was flirting with the guy a couple times. I won't be finishing that playthrough.
Sera is too child-like for me, but I have heard/read great things about her romance.
Dorian's is too overshadowed by the homophobia issue, but his character is really great, and his voice actor freaking knocks it out of the park. If i could get rid of the damn mustache (wish someone would update that mod ;_;...) I might actually complete this romance.
Josephine is simply too boring for me; I no longer even talk to her character when I play and have never completed her personal quest.
^^^all are just my opinions of course ^^ Everyone's going to have their own "best" romance...