Sure. But they weren’t coy about what the BFG stood for in BFG-9000.
The 2 biggest differences (I haven’t played all the games in each series):
DOOM: You have a health level. Getting hit lowers it. Getting medkits increases it (and sometimes spawns monsters, apparently). When it hits 0, you die. You can find multiple weapons in various categories, and they all go into your invisible backpack.
CoD: Your health bar is invisible. Hit decrease health, while avoiding getting shot heals you up to full, after a short delay. Death occurs when too much damage is done in a short period. The scifi version of this is a health bar that needs medkits and a shield that regenerates like the above. Aside from special attacks, you don’t lose health until your shield is gone. Also (don’t know if all the games are this way) you can carry a limited number of guns, usually 2 or 3. If you find a new one, you can swap it for one you have. Some newer games (not specifically CoD) may make it so that if you reload with 29/30 rounds present, you lose all 30. Conversely, walking over an ammo pickup of 30 rounds may leave 20 still on the ground if I only needed 10.
When I encountered the CoD health system, I thought it was a revelation. I don’t like scrambling for medpacks, or accidentally grabbing the SuperMegaMedkit when I have 99/100. I find that this mode of gameplay is slower and leads to more backtracking. An exception is in survival horror, Fallout, etc. where the dearth of resources is the point and you’re supposed to hoard kits. In these ones, you can usually carry them with you instead of leaving them in a pile of gore on the ground and going back 15 minutes to heal up after the boss.