For me, the biggest pro is the convenience factor. While that may seem counterintutive (since you have the inconvenience of having to change resorts), let me explain by using a hypothetical:
We have a trip planned this December with my parents. Mom is not an early riser (on top of that, they're flying in from the West coast). The rest of us are early risers (generally, RD fanatics) and our kids are young and can't handle staying up too late. We have an ambitious schedule planned. For example, we have tickets for
MVMCP and an 8:15 ADR at CRT the very next morning. We've also booked the Fantasmic Dinner Package for another night and plan to stay for Illuminations on yet another night. We also have signature dinners planned for many nights. In addition, Cape May breakfast is a "must do" for us.
We'd also like an easy commute back to our resort for some mid-afternoon R&R time (e.g., naps, pool, etc.).
How to pack all this in and still keep everyone relatively happy (e.g., mom not up too early, kids not up too late)?
A MK resort/EP resort split stay (e.g., Poly/BC, CR/YC, GF/BWI, etc.). With some careful advanced planning, such a split stay can enable mimimal commute times (less than staying at any single resort). No long waits for busses after evening shows. In fact, we'd theoretically be able to avoid the busses altogether except on our AK day.
And I don't see the transfer day as a huge problem. Simply check bags with bell services, head to a park, and then check into the new resort in the afternoon. For example, if doing a Poly/BC split, simply check bags with Poly bell services, hop on the Monorail to Epcot, enjoy a day at the park, and then walk over to the BC to check in (can even bring a small bag with swim wear into the park).
To me, the biggest downside is getting a dining plan on both ends of the split without overpaying for tickets (because, for the second leg, you either have to upgrade someone to an AP or get a 1 day MYW ticket for everyone). We do DxDP (although this might be our last time, given the price increases

). It would really be more cost effective for us to, at most, do a DP on the first end of the split and pay OOP on the second. But, with my parents, it's going to be impossible to pay OOP for any meals because my dad's likely to have a coronary when he sees the menu prices (so unless I tell him I got a special "deal" and the meals are already paid for, I'll either get a lecture about being crazy to pay those prices and/or my parents will stop eating with us).