Lambda is the most expensive thing you can do if you have more than 25% utilization. Fargate is extremely close to modern on-demand EC2 pricing (m7a family).
Right, running ECS on EC2, not Fargate on EC2. When ECS launched it only had the EC2 launch type (where as you said you must manage your machines). Fargate then came along for both ECS and EKS where Amazon managed the machines for you.