The courses are very similar, and the admissions tutor at Imperial said that too. However at Kings, they teach a module that is at the forefront of Theoretical Physics, I don't think any other UK university teaches it on a postgrad taught course. I think they teach it because it's the subject of a lot of the research conducted by the academics at Kings. Imperials academics do do research in this area but it doesn't seem to be to the same extent. And since it is in vogue, a lot of grant money goes towards this area, so will be good for my possible future PhD and career.
I've also been told that the Kings department is smaller, therefore there's a possibility that you can get to know and develop a relationship with the professors, which is important from a reference perspective. From what I've been told this doesn't really happen at Imperial, it's a bit more formal, at least for Masters students since the department is bigger.
I am really nitpicking, it's such a close call. I would love to have Imperial on my CV, but I don't think I would to the extent that I would a course ever so slightly less suited to me. So I think I am going to pick Kings.