I never played 2016, but ammo in Eternal is pretty much similar to any older Doom games, except that you also get ammo by using chainsaw on enemies. I think this made the game excellent, because it forces you to get close to enemies and use different types of attacks. There's lots of ammo if you know how to play it. The game always spawns these 'fodder' type enemies which can be used to get ammo, so you'll never run out.
I don't know, I didn't play Doom back in the day, but I did play other '90s shooters and as a general rule none of them were resource management games. The difficulty usually arises from multitasking, reflexes, and precision. They're designed so that if you use your entire arsenal situationally you'll never run dry unless you have really poor aim. The resource you do have to manage, although indirectly, is your health, because in each level you can only recharge so much before death is inevitable. DUKE3D was an exception, where on most level it would let you recharge completely at the cost of standing in one place just holding down the use key continuously for one or two minutes.
