I've used both, Kong is more "pluggable" and easier to extend in my experience. Also, the ecosystem and community around Kong is much stronger than Tyk's which is amazing.
I'd argue Tyk is easier to extend Tyk, as they include many plugins already baked-into their OS gateway. If you want to extend Kong with some custom plugins I think Lua is your only option. With Tyk you can use pretty much any programming language to write your middleware. Gets my vote