They have different uses, and in fact are pretty much opposite uses. One is effective against shields, the other against armor. One is for medium-short range, the other is long.
As far as Apogee loadouts go, you're pretty much only going to want to go 2xHeavy Blaster with the Autopulse, and Pulses or Gravitons with HIL, depending on whether you're piloting it or not, or maybe Heavy Blasters as well if you're going SO. Add a Squall launcher for the ultimate punch against big targets.
If you want a bit more fun out of your HIL, get yourself an IPDAI, set HIL to autofire, and strafe fighters and missiles with your deathbeam.
Personally I'd like to try Pulse and IR Pulse Lasers with Tachyon beam and MIRV. I'd also give the HIL to a Sunder, instead, paired with Gravitons and as many range and speed mods as I can fit.
And for those wondering, Autopulse and Plasma reach the same amount of damage done after 4 seconds, after which Plasma pulls ahead. With Extended Mags, 6 seconds. This is only against Shields, however. Depending on the level of armor, the Plasma Cannon can be over 3 times more effective.