Sure, there's plenty here that reeks of Oblivion. Parallels can be made in areas like how you interact with NPCs, or the physical character creation system, which is a modified version of what was used in Oblivion. You can play it from a first-person perspective, much like your traditional shooter. Or, like Oblivion, you can switch between first-person and third-person with the click of a button; only this time, the camera is mounted over your character's shoulder, not unlike Resident Evil 4.
But unlike Oblivion's combat system (which was entirely real-time, and involved a lot of button mashing) or your average FPS (kill everything that moves as quickly as possible, OMG!), Fallout 3 offers you choices. Want to run and gun your way through a room full of Super Mutants in first person? Go right ahead, but it's certainly not encouraged. In fact, Bethesda has implemented an in-game turn-based mechanic known as V.A.T.S. -- the Vault-Tec Assisted Targeting System.
This slower, more methodical approach to combat is actually encouraged in the world of Fallout 3, as it's more accurate and certainly more rewarding for the player. When V.A.T.S. is utilized, time stops and a zoomed-in view of your enemy appears. Different areas are displayed -- a head, individual legs, arms, a weapons, and more -- and each are given its own health meter and a percentage which represents your chance to hit (which varies depending on your stats and weapon of choice). The action can be paused at any time -- assuming you have enough in-game action points -- and actions queued up, thus opening up a world of strategic-style gameplay.