ESXi Trunk Load-Balancing with two Switches

One useful benefit of "L7" like haproxy is being able to use cookies to keep the same browser hitting the same backend server. This make debugging client hits much easier.

L4 balancing may bounce a single user around on several backend servers. (which in certain cases may be advantageous, but in a debugging/profiling sense, using "L7" is much more valuable.)

EDIT: There's also a potential speed advantage of using HTTP balancing. With keep-alives clients can establish a single TCP session to your balancer and then send many HITs without needing to re-establish new TCP sessions (3-way handshake). Similarly many LBs maintain keep-alive sessions to back end systems removing the need to do the same handshake on the back end.

Strict TCP load balancing may not accomplish both of these as easily.

/* FWIW: I wouldn't say "L7" or "L4", I would say HTTP or TCP. But I'm a stickler for avoiding using the OSI to describe things it doesn't match up with well. */

I think fundamentally if you're not sure what to deploy, go with what feels simple and natural to you. Test it (use apache bench?) and make sure it works for your needs. To me HTTP LB is more natural.

What isn't clear to me is, how many port channels do I need to setup?

One per ESXi host, or one for the entire port group? Does it matter?

You would configure one port channel per ESXi host. So, from your example, you would configure three individual port channels, each containing 4 switch ports.