MC plays back Symphony color corrections, AFAIK. You just can’t alter things like secondary CC. Source-based CC however does travel across when the sequence is opened in MC, even though MC lacks that feature.
Studio and Media Composer are nowhere near compatible. One used to be a Pinnacle product, the other is Avids core editing software. So depending on where your projects come from, you would need one or the other or both.
The only caveat would be AMA-linked clips. You won’t even need to relink or AAF when moving between Mac and PC, I do it all the time, with entire projects.