Durham is hands down a better university than KCL. In the domestic rankings Durham ranks 4th while KCL isn’t in the top 30.
That said, I study in N America and here people seem to have this perception that KCL is a first rate university. I don’t understand how KCL has come to have this high international reputation, but it does have it.
In my opinion, Durham and St Andrews are the best two UK universities after Oxbridge. But for international recognition, you’re better with UCL, Imperial, or LSE.