Depends on the guitar.
My understanding of the classic one-piece is that the SE is cast and Core is machined. I had one of each at one point. They looked VERY similar, except for the plating. The two examples I had weighed exactly the same down to the gram.
The posts are different, and the SE can have more slack, which can lead to some bridge lean. (MannMade USA posts are never a bad idea.)
The SE Paul's Guitar uses the same bridge as Core, but with metric posts.
For the more recent SE models with the adjustable bridge, I don't remember for sure, but I think they're Core parts with metric posts as well. If the bridge is different, the SE piece is really nice.