Lucifer for me. It can be used as a 1 shot kill melee weapon , and the aliens don't expect to be attacked at long range with it. Thus , with a little prediction it can take them by surprise and is more likely to kill them than the pulse.
It is sort of a flamethrower / rocket launcher hybrid. Flamethrower being more cost effective to get rid of dretches or even buildings , while the lucifer is a dragoon killer. It is best suited for battlesuits , while the pulse is better with light armor & helmet with either a jetpack or a battery pack. Generally , self damage from the lucifer added to alien attacks force the player to go back to heal before it runs out of ammo. But repeaters are still useful with it.
The pulse seems harder to master. It is of questionable use against marauders , and a bigger source of TKs than the lucifer. Of course it totally cripples dragoon attacks , but is less likely to kill them since any decent dragoon will fear pulse fire and minimize exposure. The lasgun gives more dragoon kills at stage 1. As a dretch , it seems hard to attack a pulse rifle wielder - but more often than not the human is wasting his ammo ; and again , the flamethrower is the stage 2 weapon of choice against dretches , basilisks and even marauders (very hazardous to attack humans without the zap attack)
Poll