It really depends on what you mean by "best". There are romances that have more significance to the game's overall plot, and can provide a more "complete" story relative to that position. But there are also romances that just connect better with a player for any number of reasons, plot significance be damned.
In Origins, both Alistair and Morrigan have by far the most significance to the overall story. Morrigan even more so because that romance can span two games and have some of the biggest consequences. But Leliana's romance can span all 3 games and expansions if you choose the correct conversation options, it just doesn't change anything. While it's true that Leliana and Zevran don't share the same plot points as the other two romances, they also offer their own specialness to the story. For me, I enjoy Leliana's romance because it's such a massive contrast to my warden, and they make an adorable couple.
DA2, Anders takes the cake for the most significant to the overall story, but Isabela is also a huge part of the Qunari plotline. (Plus I have to mention she's in a category I like to call "stupid hot". Big plus in my book.) Your choice in how to handle Anders and his condition, plus the final choice about his fate, are things you really can't do with other romances in not only Dragon Age, but any other video game. Hell, it borders on the kind of heartbreaking decisions you sometimes have to make in real life. But again, the other characters ALSO fit into their own plot lines and help shape the story of Kirkwall and its surroundings.
Solas in Inquisition is the king of significance. Even though he has the least content in terms of individual scenes, his presence looms over the entire game and probably the entire franchise until his plot threads are dealt with. Can't get bigger than that. But in the third game, aside from Solas, all the other companions are equal in their additions to the game, and it's entirely up to the player to choose which they like best. I personally like Dorian's the best because of its amazing writing and voice acting (a lil too beefy for me to put him in the "stupid hot" category, but he's close), but I've also had a lot of fun with a Josephine-romancing run and its terrible sweetness. As well as a Sera game with my Adaar. Although I think I find her friend-journal in Trespasser more heartbreaking than her romance-journal.