Right,
Currently on the world rankings Edinburgh stands 19th, KCL stands 21st. Both are similar in terms of prestige, so that's settled.
From an employment point of view, if you hope to remain the UK, KCL is probably better as it is in London, offering much more in terms of jobs.
If you're applying for an undergrad, you need to take into account that Edinburgh degrees will be 4 years, KCL will be 3 for the vast majority, saving you on tuition fees, however living expenses in London are greater then Edinburgh, so you need to take that into account.
If possible visit both universities, and see what they're like. KCL is urban, meaning its very divided and there isn't as much of a community feel as there is in other Unis, unless you join a sports team or a major society.
Also, read the course descriptions ( something i failed to do before whoops) and see which one you like
Peace out.