Neither Clinton nor Sanders would ever run as an independent, so they will not be facing off in the presidential election. I assume, then, that you meant to ask about the presidential primary. In that case, I think that Clinton will win for a variety of reasons.
Sanders being a democratic socialist hurts him on two fronts. First, it scares off moderates who don’t want to be associated with anything that has “socialist” in the name (even though Sanders has been very explicit about the fact that he is not a socialist). Second, it turns off actual socialists (who seem to be some of the only people in the country to realize that democratic socialists aren’t socialists).
The radical left in the US is just about as uncompromising and impossible to please as the radical right. Two people who adopt different strains of Communism, for instance, are likely to hate each other even more than they hate Republicans once they get talking. So the idea that there will be a coalition of leftists rallying behind Sanders is laughable. They’re too busy explaining why he’s not their candidate to think about whether or not he should be (imperfect representative as he surely is for their various causes).
Clinton won’t be winning the radical left either, but she will be getting a hefty majority of the moderates (particularly once the vanity candidates drop out). She’ll also be getting the people who just want to win and think that she has the best chance for victory when the actual election comes about. And the people who think it’s about time we had a female president. And the former Biden supporters. And the right-leaning Democrats who don’t care (or secretly like) that she grew up a Republican.
But the main reason I think Clinton will win has nothing to do with this sort of predictive analysis. It has to do with the numbers. While Sanders is doing well in places where the media likes to focus (e.g., New Hampshire), Clinton is dominating when you look at the primary race at the national level. Furthermore, she’s vastly more popular among women and minority voters (whereas nearly all of Sanders’ voters are young, white, and male). And she got the largest boost in the polls after the debate. The only real question is whether she’ll decide to be more gracious than President Obama and ask Sanders to join her on the ticket.