I honestly asked this question myself in the DO Students forum, should be on page 1 still.
From what I gather though:
For preceptor-based, you are assigned to a single doctor. You go with them to clinic, hospitals, teaching at AZCOM workshops, etc. If you get a really cool attending who wants to teach, you may have a great experience and get a great LOR. However, you might get one who wants to treat you like a scribe, or sends you home in 3 hours without learning anything, or you may just not click and you're stuck with them for 2-4 weeks.
Residency-based, exactly what it sounds like. You go with the whole program, so you're alongside the residents as well as the attending. Apparently this is better for learning how to be a resident and doing well on audition rotations and sub-Is in 4th year. You can also fish from a bigger pool of people for a LOR if you want one for that specialty.
Residency-based is a bit less paperwork and whatnot, and you get to stay put (if that's your bag) - you're only being credentialed for one hospital system, learning one EMR, etc. Preceptor-based, if your surgeon attending operates out of 3 different hospital systems, that's a bit of a pain, but it could also expose you to a lot of different work cultures and such, if you're interested in residencies that are in any of those hospitals.