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The first question you have to raise is what you want to create since it makes the decision between them both much easier. Also you should know if you just want to make your project for fun or buisness. For example if you want to create a high end graphics shooter you better use UDK since it has many source files from Unreal Tournament to expand on but more important you can achieve nice graphics in a few clicks for free. If you would create a shooter in Unity you have to create many things from scratch and without Unity Pro the graphics are limited. I mean the UDK Samaritan demo shows it all:
So these are just some examples I would create with them but notice this "You can make every game you want with both engines!"
Both engines have there advantages and disadvantages in the end it depends on three main
questions you have to ask yourself:
With the last question I mean do you know anything about things like programming, modeling or Level Design because for the UDK a basic knowledge would be better to make quick start since it is a complexer engine (to learn) than Unity. Otherwise in the UDK its much easier to create levels and design environments if you are a beginner. One thing I just mentioned briefly are tutorials and community both communitys have there advantages the UDK has many free starter kits and the awesome Epic games forum Unity3d has frequently Live streams and a short question forum named Unity Answers. The last thing I want to mention is that UDK is more used for bigger or expert projects (e.g. Outlast as a expert project). Unity instead is more used by small Indie Developer (e.g. Slender). Anyway these factors don´t make a engine good or bad it all depends on you and your decision.
I hope I could help you somehow and for more questions on this topic you can contact me on: