UDK and Unreal Tournament 3 are both powered by Unreal Engine 3.
Some people referrer to UE3 as Unreal Editor 3, but UE3 stands for Unreal Engine 3. There is no such thing as Unreal Editor 3; Unreal Engine 3 Editor would be more accurate.
So, Unreal Engine 3 = UDK and UT3.
Unreal Editor interface between the UDK and Unreal Tournament 3 are essentially very similar. There are differences of course, but if you work with Unreal Tournament 3 you'll have no problem working in UDK and vice versa.
Majority of tutorials for Unreal Tournament 3 Editor will work with UDK.
Lots of models, textures, particles, vehicles, weapons.
Large community of maps and people creating maps using Unreal Tournament 3.
More modifiable with the content already included within Unreal Tournament 3. You'll have access to all the source code files for weapons, vehicles and characters in Unreal Tournament 3. Unlike UDK, where you will have access to very limited amount of weapons and vehicles.