When comparing ELB vs HAProxy, the former can feel a bit limited as far as load balancing algorithms are concerned. It supports only round robin and session stickiness. But consider cases where you need to load the balancer based on incoming URL, or on the number of connections to be handled by individual underlying servers. HAProxy can handle those, and more.
AWS charges you for each hour or partial hour that your Elastic Load Balancer is running, and for each GB of data transferred through your Elastic Load Balancer. Since HAProxy is open source, on the other hand, setting it up and running it on an EC2 instance will cost you nothing more than the normal instance usage.