Gamebryo is a middleware game engine designed for portability across PCs and consoles. Older versions are compatible with Xbox, PS2, and Gamecube while newer versions only support 360, PS3, and Wii (and PC of course). It used to be called the netimmerse middleware and was used for Morrowind (which is why modding for oblivion, FO3 will be familiar to those with experience modding Morrowind) and obviously Bethesda highly customized it to suit their needs with Oblivion/FO3/NV. That's pretty much how most game engines are made, same with Unreal Engine 3 which is based on version 2 which is based on the original, modified along the way to take advantage of the latest tech. Then somebody licenses it for their own use which may or may not work out so well (Square's last remnant being a good example, silicon knights complaining how difficult it was to use the engine and suing epic). Source is actually a highly modified version of HL1's engine which is based off of Quake 1! Modern Warfare 2 is a highly customized Id tech 3 engine. Capcom's MT framework is based on the PC port of Onimusha 3 if you can believe that
The engine we're familiar with from Oblivion and FO3/NV is obviously a highly customized (by Bethesda) variation. I don't see how people can honestly say it looks 'bad' at all though or even 'showing it's age'. Compared to what? It's better off than the Euphoria engine that runs GTAIV and RDR except those two can pull off environment shadows with little hit on performance. That's the only thing I can really notice with gamebryo in FO3 but supposedly they were there at one point and the performance hit was too hefty.