Is the UDK better than Unity 3D

It's really all about your personal preference:
The Unreal Development Kit (UDK) The UDK (powered by Unreal Engine 3) is definitely the best choice if your game relies highly on graphics, however to unlock UDK's full potential, much reading and time must be spent as the UDK (or Unreal Engine 3 development in general) has quite a steep learning curve.
 Unity 3D Unity 3D is an engine that is aimed at making game development easy, everything is built into the editor, it's documentation is simple and easy to understand and it supports many different scripting languages, it's graphics are decent, and run on lower end computers.
 Price (UDK vs. Unity 3D) In terms of price, it's also up to you, Unity 3D is free, although there are certain graphics features that are for Unity 3D Pro users only, such as advanced shaders. UDK is free for non-commercial products, individuals or companies looking to sell a game commercially must purchase a commercial license. Epic Games collects royalties on your game sales, 25% on profits over $50,000.

 Platform Support Unity 3D boasts a wide range of platforms that are available for publishing, currently (As of February 4th, 2011, Unity 3D supports the Web, PC/Mac, iOS, Android, Xbox 360, and PlayStation 3. However additional license fees may apply.) The UDK supports publishing to Windows PCs and iOS devices. Currently UDK, nor does UnrealEd have support for Mac OS X, and Epic has not announced plans to support either at the moment, however Unreal Engine 3 does support Mac O S X. As of the September UDK update, UDK supports publishing to Mac OS X.

 Conclusion It's all up to you, if your game relies heavily on graphics, go with UDK, however if you are not a professional, or you don't have a previous background in game/Unreal Engine development, it will take a while to learn. If you are looking for an easy way to develop a game, or sell your game without paying any license fees and paying royalties, than Unity 3D's free version would be best for you. If you want to reach a large mobile audience as well (Android and iOS), then maybe Unity 3D will be for you as well.