Tyk offers a more “batteries included” approach to Kong, and so doesn’t rely on external plugin authors to extend the ecosystem. 100% of our dev team are constantly working on our open source components and we like to keep it that way.
Because of that, Tyk isn’t “open core” like Kong is, there’s no lock-in or levers to get you to buy our value-adds like our Management Dashboard GUI or our Multi-Data-Center clustering add-on - you should be able to do all API Management without having to pay us a penny.
A simple example is OpenID connect support, this is a Kong enterprise plugin, with Tyk that comes as part of the normal gateway.
In terms of performance Tyk and Kong are pretty close now (Tyk pre 2.6 was slower) but we believe we now have parity, especially when switching on things like analytics, auth and rate limiting.
Tyk works very well in k8s though we don’t have a helm chart yet (coming soon).
You can also deploy Tyk as pure SaaS (fully managed), hybrid cloud (we handle back-end and control plane, you install gateways local to services) and full on-prem (install anywhere: K8s, AWS, GCP, Azure - even on Arm servers). We’re unique in that regard.
Tyk has always been separated into control-plane and operations-level components (our gatewaybis very small), so we don’t see that as something new to crow about. If you use our Dashboard, it moves the configuration and data layer out of the gateways and moves it centrally. If you use our MDCB system (enterprise) you can extend that capability across clusters in different clouds to get really targeted, distributed API governance.
There’s a bunch of other things that are different too, but they are more functional.
I contacted Kong sales once about OpenID connect support, they basically dismissed us as too small. Needless to say we took Kong out of our stack and won't consider it again.
I work for Kong and I am an author of that enterprise OpenID Connect plugin. Maybe that is a biggest exception to me, as otherwise I'd say that almost all of my code and related goes directly to OSS.
OT: Your frontpage is very slow (Chrome v.71) - it loads but takes ages to scroll down.
Single language simplified our architecture, less plugins created less bloat, and ultimately we moved faster with Kong.
Engineers also really enjoyed that they got to learn something new and also could get into C easily with Kong as well using LuaJIT.
Kong is arguably more popular than Tyk (and other similar gateways) when it comes to adoption (55M+ downloads and more than 70,000 instances of Kong running per day across the world), and faster when it comes to performance. BBVA - a large banking group - wrote this technical blog post a while ago comparing Kong's and Tyk performance: https://www.bbva.com/en/api-gateways-kong-vs-tyk/\
Kong OSS is 100% open source, not limited to non-commercial use.
Kong is basically a programmable runtime that can be extended with Plugins . There are more than 500+ plugins that are available on GitHub that we are (slowly) adding to the official Hub, among over 5000+ contributions. You can talk to the community at https://discuss.konghq.com/
Kong is also lightweight with a lower footprint, which is required to support both traditional API gateway use cases and modern microservices environments (Kubernetes sidecar, for example). Because of that, our users are basically using one runtime for both N-S traffic (traditional API Gateway usage) and E-W traffic within a microservice oriented architecture. You can easily separate data and control planes to grow to thousands of Kong nodes running in a system.
There are users/customers running 1M+ TPS on top of distributed Kong clusters spanning across different platforms (containers, multi-cloud, even bare metal) with less than < 1ms processing latency per request. One of the reasons for this is that with Kong you can include/exclude plugins that you don't use instead of having a heavier all-in-one runtime like many gateways do.
As a result to Kong's adoption, the business is also growing very rapidly which will allow us to better deliver OSS features moving forward :) 
You can ping me at https://twitter.com/subnetmarco