MLIR maintainer here, or however close one can be given that we don't have a clear ownership structure. This has been discussed repeatedly in the community, and it is likely that many things will get eventually ported/reimplemented, but there is no strong push towards that. Lower level parts of the stack, such as register allocation / machine IR / instruction selection are where LLVM has seen a lot of investment are unlikely to move soon. At least not in a generic way.

There was a keynote at the LLVM developer meeting a couple of years ago presenting the differences and the likely evolution from somebody not involved in MLIR that does the lay of the land.