Which one to choose ?
Usually, APIs with light traffic are more cost-effective on API Gateway, while the high-traffic ones can find cost savings by adopting an ALB instead.
API Gateway
Technically speaking, the main limitation of API Gateway is the timeout of 29 seconds. If a request takes more time to be processed by the backend resource (e.g. a Lambda function), the API will respond early to the client with an error.
Although there is a limit in the number of requests per second, as mentioned above, it can be increased according to the demand.
Suitable for small teams that want to reduce time-to-market, as well as sophisticated use cases that require complex security measures and access control logic.
Load Balancer
Can scale to hundreds of thousands, or even millions of requests per second, without any issues.
For that reason, an ALB is more suitable for low-cost/undifferentiated applications, long-running processes, and/or ultra-high-throughput applications.