All my life I have stayed away from the 720° clutter that MAME generates, and now with RetroArch I find myself in the need to immerse myself in this “experience”.
2003-Plus is the same as 0.78, although it is totally different…
MAME 2003-Plus is a fork of MAME 2003, which is a fork of Xmame 0.78 (an unix-like port with portability in mind) and this in turn is a fork of MAME 0.78. But it has a code rewrite that makes it practically an independent project. I think it should have another name.
As @Jamirus tells you it is compatible with original 0.78 romset, better said, they have given support to almost all of it. But 2003-Plus has added support for new games, fixed bugs and added improvements.
The most outstanding differences are, that you can create/use custom soundtrack and in high quality (I think it is the only MAME that does it). The options are adapted according to the characteristics of the machine, and can be saved based on that set.
The current 2003 fullset (0.78) supports 4727 (2314 parents) and 2003-Plus supports 5213 in total (2498 parents).
And not to mention, the support and integration with the RetroArch ecosystem.