It really depends on their personal power and skillset. You can only use what you have to work with when you activate your death curse.
Someone like Harry, who is both powerful and extremely well-versed in fire magic could probably call down something like a massive firestorm on someone if he was so inclined, but using the same amount of power with gravity magic would accomplish much less of an effect because he is barely proficient with it.
Canon Molly, on the other hand, was less powerful but also more subtle and skilled at working delicate effects like veils. She might not have been able to outright incinerate someone with her death curse, but she could have put a really fucked up and likely permanent illusion or mind-affecting effect on them, like turning all pleasure into excruciating pain or forcing them to see the world as if everyone, including themselves, were rotting corpses shuffling around and groaning miserably at one another.
Whoever this enemy caster is, it's highly unlikely that he's a White Council level practitioner, so his power is going to be limited, and his go-to magic, both for preparing to fight by priming his minions and for attacking our group, seems to revolve around either enraging the target or slipping a rage spirit into them. If he can even pull off a death curse, chances are he would reflexively fall back on what he knows best and try to drop an amped up version of it on us.
Again, this is assuming he even has that ability. DF doesn't put much focus on them, but the world is full of lesser practitoners who have too little power to get White Council attention. They can accomplish minor magic effects, like simple rituals and the like, but they also often have one or two tricks they've focused on really heavily, to the point of being a real threat in some circumstances. It's far more likely that our enemy falls into that category.