The benefit of using Kuma + Kong Gateway are:

Feature-set: Kong + Kuma provide an end-to-end solution for both APIM and Service Mesh with a feature-set, and a performance, that is not matched by AWS services. In addition to this you can extend Kong Gateway with 70+ plugins out of the box and choose between 500+ plugins from the community to cover every use-case. In comparison, the feature-set of AWS API Gateway is quite limited and basic.
Performance: Especially in the case of Kong Gateway, performance has always been a top priority for the project (more performance deliver more reliable applications). In some benchmarks the latency added by AWS API Gateway can be 200x more than what you would achieve with Kong Gateway natively which has been hand-crafted for maximum throughput.
Cost: While cloud vendors like AWS make it very easy to get up and running with their services at a lower initial cost, that cost ramps up very quickly (exponentially) as the number of requests are increasing. With Kong GW you don't have this problem, since you can run tens of thousands of concurrent requests on a small EC2 instance (or Kubernetes Ingress, via the native K8s ingress controller for Kong Gateway).
Portability: You can replicate your infrastructure on any other cloud, or on your development machines with ease. Want to run your gateway + mesh on your local Kubernetes cluster? You can do that. Want to run your infrastructure on another cloud provider? You can do that. Strategically you have full ownership of your infrastructure and its future. When it comes to Kuma, you can also run a Mesh on VM-based workloads in addition to Kubernetes (Kuma is universal).
And much more.

Disclaimer: I am the CTO of Kong.

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