The problem with Fargate is the cold startup time and lack of support for GPUs. It's also quite new and there's all sorts of issues with it but hopefully will get resolved.
I think ECS is a better fit if you require GPU or you can do with not scaling to zero. Obviously once Fargate catches up and polishes its kinks it would stand on its own but given the way Cognito is, I have very little faith that things will improve quickly (theres an open ticket in cognito that is over 3 years old).
Cold start would be just as much of a problem on lambda, no? Which is to say, it would or wouldn't be a problem depending on your needs modulo language/runtime choice. If we expect to compute for >15 minutes, cold start is probably not a big deal.
I think ECS is a better fit if you require GPU or you can do with not scaling to zero. Obviously once Fargate catches up and polishes its kinks it would stand on its own but given the way Cognito is, I have very little faith that things will improve quickly (theres an open ticket in cognito that is over 3 years old).