Unreal Engine 4 or Cry engine 3. Why?

UE4 has more learning materials, plus it’s cheaper, and it’s improving all the time. You can also interact with the engine developers to find fixes for problems and suggest things you’d like to see.
It’s also cheaper, with Cryengine you lose access entirely if you cancel subscription, with UE4 you can pay for a single month and you still have access to that version if you cancel. Plus Cryengine requires an additional licensing fee for their audio system.
The main advantage to Cryengine I think is that their lighting system is easier to use, no baking required though you don’t get the option to have high quality static lighting.