Why not UDK?

Unity vs. UDK
As of 3/6/2014, the Item Creation Team has determined that UDK is not capable of performing the item creation methods we need to complete this project. The following links relate to our investigations into this functionality: Dynamic Arbitrary Geometry Control

We thought we might be able to do a workaround by implementing our own Physics class, since those can at least deform existing geometry. Here's what we found: Implementing custom physics in UDK

The bottom line is that UDK does not support dynamically modifying in-game geometry. Matt and Seth have scoured UDK's UnrealScript and C++ APIs only to find that all such functionality, if it exists, is deliberately hidden from developers.

Unity, on the other hand, does provide this functionality, as seen in its program documentation as well as in the following video tutorials:

Generating Mesh Geometry Procedurally

Video: Creating meshes procedurally