I haven't rebodied any mod dolls onto Fashionista bodies yet, but I have rebodied some of the 80s Barbies and newer dolls that came on the Model Muse body. I prefer the more posable bodies (Model Muse can't even bend their knees).
In fact, I really like the body that they made for some ballerina and basketball dolls in the 90s but I only got 2 of them and didn't get any spares to rebody other dolls.
Some of the mod dolls I bought I just bought the heads because they were for sale at a bargain price, so I have put those on more modern bodies and I think it's just fine, although sometimes the older heads have faded or discolored so the skintone color match is not perfect.
Wouldn't it be great if Mattel sold separate bodies for re-bodying like Integrity Toys did a while back. However I think Mattel really underestimates how popular articulation is amongst collectors!
I have seen the Mod Barbie head on the Obitsu body, I loved it. The articulated dolls are good for the posing but I really like the vintage dolls.
I have just one Obitsu body and I love it. I would definitely recommend it.