That's not quite how game engines work.
In order to make Dragon Age Inquisition, Bioware had to take the Frostbite engine and pretty much flip it inside out to make it RPG-friendly... they made exponentially more changes to Frostbite to make it accommodate Dragon Age, than Bethesda did to 'update' theirs to serve the needs of Skyrim.
And yet everyone, including Bioware themselves, still refer to it as the Frostbite engine. Because at its core, that's what it is. It isn't a different engine just because they added to it, or changed stuff about it.
In fact, the flexibility of a game engine is a huge part of what defines how good it is, or isn't.
You can take a Mustang and upgrade its engine, give it explosive tires, a fire-spewing exhaust, bulletproof windows, spikes in the trunk, etc... but at the end of the day, its still a Mustang. It doesn't become a new kind of car because you welded a bunch of shit to it.
Bethesda did some great things to the Gamebryo stuff in between games, Skyrim is certainly a notch above the Fallout 3/NV games in a number of regards. But at its core, its the same engine, and likely the one we'll be staring down when Fallout 4/next/whatever arrives.
Make no mistake, though - recycling an engine is a good move for a developer to do. It cuts down significantly on development time and expense, and Bethesda takes long enough to make their games as it is.