I am currently an MTS student at Harvard, and here are my (highly speculative) thoughts on your situation, based on my own observations:
-At our school, just about everyone seems to get some kind of funding. The lowest I have heard of is a half-tuition grant. There does not seem to be a preference for either degree.
-The coursework for both programs can be quite similar based on area of interest. At Harvard, the MTS is only 2 years, while the MDiv is 3 years. That extra year can be a huge advantage in sorting out your interests, building your credentials, etc., if you have ANY interest at all in this sort of work, go for it. You also get set up with fieldwork opportunities, and if you go to a school with money, you may be able to do something really amazing, even overseas.
-It is my personal opinion that applying to both programs within the same school does not make much sense. The admissions criteria are relatively similar.