Lots of similarities. Oppresive atmosphere (both done by shutting off lights, claustrophobic areas, etc.), both take place in space stations and planets, both have organic and gruesome looking enemies, multiple pathways in levels that require x item to progress (in Doom's case keys while in Metroid's case missiles, etc.), similar protagonists (barely speak, are all alone, are intimidating, similar armor design, etc.) and even the final boss in both games is a mechanical brain... oh and both games have good music too (many times both trying to be creepy).
Coincidence?