neither is designed to take advantage of the most modern video cards like Skyrim does, but the engine can be modified easily enough.
It does? Skyrim was released very late 2011 and it uses D3D 9 (and nothing else). Doesn't has any occlusion effect (5 years after Crytek introduced it), nor atmospheric scattering, nor volumetric lighting. Supports up to 4 shadow casting lights, they're really bad quality and they're all selected by hand (so the level designer has to mark which lights cast shadows, which meshes cast shadows, and pray it doesnt has more than 4 in the same scene, no dynamic LOD of lights or anything, just distance based).
All water in the game is represented with a flat plane and watery normal maps on top of it (again, Crytek in 2007 did it much better). Most of the things in the world dont cast a shadow, like clutter and medium sized rocks, which CryEngine did in 2007, also GTA IV in 2008 did actual ocean waves AND the whole open world shebang, procedural cluttering, real dynamic shadows, you name it.
Whatever animation system or blending system it has is straight from 2006 (or new but very badly used). Most "advanced" part is that feet accommodate along the floor, a bit, so most of the time everything looks as if its floating on the terrain.
It apparently can use multiple threads, but it keeps one or two to 80% utilization, rest unused.
Unity/UE4 can do any of those with ease. Skyrim was anything but technically advanced for its time. Default UE4 shooter scene thingy already looks better and is better animated than Skyrim.
The places where you are going to have a problem arent the big "systems" (rendering, physics, sound, animations), those are well covered. You're going to have issues with other things. Managing the world data, LODing systems, daily AI routines (did any game had that before Oblivion in 2006?), and also a very important thing: Modding API.
UE4 and Unity are really hard to mod. Skyrim's engine is practically made to be modded. It has its own versioning of world references, so plugins that modify the same things can overwrite eachother depending on some order and keep working. Literally the game updates are stuffed in an additional plugin, like any mod, that applies over the base game and the engine just fucking picks it up and makes everything work. Its awesome. Last time I checked they also implemented hot reloading of plugins, in the shipped game!
Also load times are really tiny. No clue how they do it, but quick save and quick load work really well.
EDIT: Oh and they have their own seemingly asynchronous scripting system, works really well, and a huge event system to fetch data from and run those scripts. Very nice stuff.