Disclosure: Community contributor to HAProxy, I help maintain HAProxy's issue tracker.
> For my mental model, nginx is the right choice for SSL termination, logging, request mangling, interpretation of cookies and loadbalancing based on request information (for example choosing haproxy instances based on a domain name).
HAProxy can do all that and IMO it also does it better.
Personally I chain HAProxy and nginx in reverse order: HAProxy exposed to the Internet, doing all the heavy lifting. (Multiple) nginx with minimal config as a static file server and FastCGI gateway behind HAProxy.