I had to make the same decision and I'm international too. The fees for imperial are so much higher than kings but ultimately I decided on imperial because when I went for my interviews, I just liked it more personally and felt like I would fit in there better. although kings is a nice uni too and has a great reputation for medicine.
I wanted to do an intercalated BSc anyway and its possible to do it at kings too and I think that year costs like 15k so the difference was 65k more for imperial for me so is that something you'd like to do?
In terms of reputation, it really doesn't matter because you're going to be a doctor anyway and they're both associated with amazing hospitals plus its London so you can't go wrong with either.
Congrats on both your offers and good luck with choosing one!
Oh and if you choose imperial, join the fb group
Half of the top 10 aren't even RG...