The main problem you'll face is the increased workload you'll face in preparing your application materials. Depending on the programs, you'll often be expected to identify faculty you'd be interested in working with, and you'll be expected to succinctly show why your research interests fit with that person. The statement will also be viewed as a whole, so you will inevitably need to either focus a single application around certain aspects or be clear that you are open to a range of sub-fields within a given discipline.
Some people like very focused statements, while others are still welcoming of more broadly stated interests, so one is not necessarily good or bad. That's part of your unique situation and interests, but the advice I've been given is if you really do have broad interests, express that because it will attract advisers and programs that value that. But if you really only want to study certain things, say that because that too attracts you to the right people you're more likely to be happy with in the long run.
Most people (all I've talked with, anyway) find preparing multiple drafts of all the materials stressful as it is, so having to prepare multiple versions with very different tones and a different focus likely will take you some more time and effort to do well. So if you are applying to only one sub-field per application you can still focus your statement on that field and just the right people to work with in that field - but you are going to have to create at least 2 sets of very different personal statements, each of which will be customized per program.
As long as you are OK with the extra workload, I am not aware of any other downsides beyond application fees if you are applying to more programs in total. Applying to programs with different sub-fields is fine if you really interested in both, and will not generally make you a less attractive candidate because no one but you (and maybe your letter writers) has any idea you're applying to a variety of programs.