Well....in all honesty, an argument can be made. For all the good Doom did, it was essentially just a re-skinned Wolfenstein, which if we're talking about influence, should be above both, but I would personally put Goldeneye over Doom in some respects.
Before Goldeneye, FPS's for consoles, were like platformers for PC's. Few and far between, with the ones on them being shit, or shitty ports. Both had the same problem. The controls. A keyboard sucked for platformers, and a control pad sucked for shooters. Goldeneye changed that problem for consoles. It revolutionized that portion industry, and broke the door down. Without it, it's hard to say if the industry would've ever figured it out, and if the game that truly busted the door wide open, Halo, would've even be conceived for a console.
Where I would give Doom the nod, is in how it's aged better. I can still pick up and play Doom in it's original form, and have fun with it. Not so much with Goldeneye, as it's then revolutionary control scheme has been refined, and greatly improved upon. Playing it today on the N64, and it's hard to imagine how we ever played it in the first place, with it's one analog stick. It's level design ain't exactly the tightest either.