The antonym to strong is weak, not nice. I think people often forget that girls, particularly sane and intelligent ones, do not reject the prototypical "nice guy" because he is nice but because he is a pushover. That is, weak. You can be strong and nice. In fact, I think the strongest ones usually are "nice" or considerate because they can afford to, whereas at least where I'm moving, being an asshole or abrasive is a sign of weakness.
In my experience, girls do want first and foremost an alpha male, and being a nice guy on top of that makes it even better. It's just not a necessity so the jerks can succeed without that quality, whereas the nice guys can't succeed without "dominance."
I'm sure you have friends who you would consider incredibly nice, but very shy, guys who never could get a girlfriend, and plenty of jerky, but confident, guys who you wonder why girls would date. Confident guys, even when not nice, just seem to win out over really nice, but not at all confident, guys. Guys with both win out over both. Whether or not it's a bad thing is your call.
(I'm not arguing guys are above their primitive desires: not by any means, it's just not the focus of this discussion.)
I guess now we know what time_management's new nickname is...
If a woman has a preference for muscular men, or skinny hipsters, or even fat men, that's fine. We all have our physical preferences. And the fact that women want to date men with enough spine to have meaningful character is a good thing. However, women who are attracted to loud, boorish, and stupid badboys are utter garbage.
The attraction to badboys is not aesthetic; many badboys are out of shape and ugly. I think the appeal of the badboy is that it provides release from the pressure that is put on women to "marry up". It's not looked down upon for a man to marry a woman less ambitious and intelligent than he is, as long as she's good on her own merits (e.g. if he's a Wall Street quant with a 155 IQ, and she's in a lifestyle career and has a 130 IQ, that's fine, because she's still a smart woman who can hold her own in intelligent conversation). Women, however, are expected to marry men with at least the same level of earning potential and intelligence, because of a lingering concern with gender roles and the expectation that the man will be equal or dominant. This obviously places a lot of pressure on high-power women. The appeal of the badboy is that, although he's virtually never intelligent or ambitious, he's dominant on account of his sheer arrogance and narcissism, but at the same time worthless enough that he can be flippantly discarded. This enables the woman to enter a relationship where she takes a submissive role, but one that has an "off switch"; she can leave without pain, since it's unlikely that she'll form an emotional attachment to such a useless and defective man.
[*Edited for clarity @ 12:26]
I actually think men get some blame for the "girls falling for aholes" problem. I think too many quality men listened to their mothers and school teachers, who said the key is to be a nice guy. The assholes never listened, and learned on the street to win girls via strength. Thus only the assholes act strong and get the girl, while the nerds lose out. The solution is that the good men need to grow a backbone. Then women will be able to find men who they are both attracted to and are good partners.