I, like pretty much everyone who has seen Les Miserables, am a firm supporter of Team Eponine. I fangirl Lea Salonga, I love On My Own, and my gut reactions sort Eponine and Cosette into "the awesome one" and "the annoying one."
It's easy for me to understand my love for Eponine. She has great songs, she's sympathetic, and as the brave girl suffering under unrequited love, she's fairly easy to connect with and hope for happiness for her. The general dislike of Cosette is harder to understand, because... well, because there's not much there to dislike. And that is, I think, actually the reason why Cosette is so unpopular. She has little personality and little struggle of her own. She's a cipher, a plot device, so that Marius can fall in love, so that Eponine can have more conflict, so that Valjean can struggle and have a reason to join the barricades in the second half of the play. And when a cipher seems to float into a position (or in this case, a relationship) that a more sympathetic character has strived for and failed to get, it is more than easy to dislike her, because she has no personality or struggles of her own to recommend her.
Young!Cosette is quite sympathetic, even heartbreaking, but if I were asked to describe adult!Cosette, I think I would get stuck on "blonde." Perhaps I could expand it to include her rather high-pitched singing voice, and throw in "loving daughter" and "in love with Marius." The song In My Life makes some effort to throw light on her generally isolated life and her frustration that her father is keeping secrets from her, but I think these details are quickly lost when the song merges into a love song with Marius. As an adult, her entire presence in the story involves seeing Marius, falling instantly in love with him, singing a song about it, and then getting married at the end. Happiness seems to come easily to her; her romance is unbelievable, and her pure sweetness and fairytale fortune seem rather out of place in an otherwise dark and bitter world.
I find it interesting, and a little disheartening, that it is so easy to dislike a female character who isn't really a character at all. It's not that her focus on romance makes her too "girly," since Eponine's highly sympathetic plotline also involves her love for Marius, but that, without the depth that other Les Miserables characters receive, it's too easy to dismiss her into a dislikeable feminine trope: the simpering, unworthy other woman. There's little evidence to support this conclusion, but there's also little evidence to disprove it, and so a viewing public that is both used to these kinds of simple categories and immersed in a show where most people don't get the happy endings they would seem to deserve, are happy to dislike and dismiss her.