On one hand you have a docker image with your source code/static binary baked in. The other you have your source code/binary encapsulated in a serverless framework (with an Event handler of sorts as your input).

The container doesn't lock you into a particular ecosystem, but hasn't solved how you deploy and run your container (Heroku, managed k8s, AWS ECS/EKS/Fargate). Serverless on the other hand will give you a runtime for your API and allow you to go live (assuming you've setup an account or whatever).

To migrate something that already works to serverless is a bad idea. Maybe if you're pretty comfortable with serverless frameworks and you like to hack a lot of projects up quickly, sure serverless might be a good fit. But why not instead start off with a container? At least you have the flexibility to run that on whatever you damn want - Even a t2.small instance with a docker daemon running.