As a job, I don't have anything against prostitution. My problem with the idea that a woman who has a lot of sex is a whore is that I think it's pretty sexist. It seems to imply that a woman cannot possibly enjoy sex for sex's sake, that she's doing it only for the pleasure of her partners, and that what she gets out of it HAS to be money, because it can't possibly be sexual pleasure. I find that attitude very sex negative.
At least a slut is someone who has sex because she wants to, even if it's apparently a bad thing to have sexual appetite when you're female. That's why I think it's preferable.
I know that in reality, someone who has sex for money can very well be doing it because they want to, have made the decision to, etc, and that it can be very sex positive and healthy, and that as you said it's a service like any other. That's not my problem. My problem is the implication that if you are female and had more than X partner, then obviously you weren't having sex with them for the sex or out of love, but because you wanted to manipulate them with sex to get something else that you wanted.