Plasma vs. HIL
One thing that is seldom mentioned that often very heavily influences my choice between these two, is that plasma cannot be left alone. It needs constant supervision due to it's huge flux generation.
AI ships cannot be trusted with plasma, and will almost always run up thier flux, and die due to overload.
Enemy ships with plasma are somewhat easier than any other large energy for the same reason.
It may be the better weapon for raw damage output. But I consider the HIL to be the better general purpose weapon because it can be left to do its thing in an automated group, or on an AI ship and still perform very well with easily managable flux generation. Plasma can't do this, and is relegated to specialist (usually player only) loadouts which are built around the weapon.
Also, HIL is hitscan, or very nearly. And the beam can be steered into things (even when being fired from automated turrets) which is not something projectiles are capable of.
There's also micromanagement to consider.
If I want to control the missiles on my ship, then that ship will almost certainly not have a plasma cannon on it. They create too much flux to be automated, and undermine any shield tanking ability the ship may have. And if the ship has a mobilty system this can have an odd interaction with the projectiles which mean shots routinely miss, wasting flux.
Conversely, if I want plasma on my ship, the rest of the loadout will be either empty slots or PD.
I'd consider them to be the other way around to most people.
HIL = general purpose
Plasma = specialist