I applied to Kings as well. It's a really solid school with some unique curriculum choices. As I'm sure you've seen, Kings's strength seems to be in its War Studies department, so I think if you were looking to study conflict, KCL is the clear winner. It's also in a really excellent (but somewhat pricey) part of London. And London would really be an experience in terms of connections and career resources, etc.
Unfortunately, I haven't heard of Miami's program, bur I hope this helped a little!