Jerry T.
The midijay plus is actually bassed off of the SD5 engine (with some modifications ofcourse), while the Midijay is based of off the XD9. Now, as technology progresses, it becomes harder and harder to maintain compatibility with older products (SD1/SD1Plus). For this reason , most of the SD1 series styles loaded into a Midijay are 'more' compatible that if loaded into the newer Midijay plus (that has newer sounds and newer drum loops). You will have to manually go in (press EDIT when the STYLE button is lite) and change the style parts (re-voice), including DRUM 2 (where the audio loops reside) to modify the style ... an issue that is avoided on the Midijay due to similarities with the SD-series.
As for registrations, no, they are not compatible (different sound engine, different operating system).
Thanks,
AJ