Thank you, Leon, for your detailed answer.
I have to say I missed that part about Kong relying on OpenResty and Nginx. That was a good point.
Performance-wise, though, I came across that benchmark, done by a spanish banking group, late last year:
They seem to have noticed that Kong was able to handle significantly more requests per second than Tyk.
For that, we will surely have to test this ourselves.
Please feel free to comment on that.
Anyway, I greatly appreciate the time you spent to answer my question.
I will now move on to find more info about your comments.