It's a combination of factors. The therapist doesn't have to, and won't ever be perfectly prepared to deal with your issues, but specialists can typically provide more and faster results, just as a math teacher can explain Algebra more efficiently than a first grade teacher who's a generalist. However, the relationship is also a critical factor, key to healing, so you must balance for yourself how good the relationship is- how much trust you have, how much connection, how much respect, how much history, etc.

If you have not seen her for long, and are not deeply attached, I'd definitely recommend seeking a specialist.

Yes, therapists can come up to speed in multiple areas, but you can't substitute 10 years experience with eating disorders, for example, with skimming the latest research and reading books or even consulting with a more experienced therapist. There isn't a substitute for depth of experience, just a matter of what you need most right now and how specialized your issue is, and your practitioner's experience level.

Best of luck, trust your instincts.