Both OpenJDK and Oracle JDK are created and maintained currently by Oracle only.
OpenJDK is the default version of Java that Ubuntu uses and is the easiest to install while Oracle Java 7/8 is Oracle’s own version of Java 7/8.
It entirely depends on the target platform on which you want to run JDK. Technical differences are a consequence of the goal of each one (OpenJDK is meant to be the reference implementation, open to the community, while Oracle is meant to be a commercial one)
They both have “almost” the same code of the classes in the Java API; but the code for the virtual machine itself is actually different, and when it comes to libraries, OpenJDK tends to use open libraries while Oracle tends to use closed ones.
OpenJDK was reported to work better for large number of users with small request count, while it become worse for small number of user with prolonged. This is an undocumented behaviour, and never seen anywhere other than experienced on some J2EE containers.
I choose to install Oracle JDK, since there were complaints about using OpenJDK would meet bugs sometimes. (See this post if you decide to install Oracle Java 8 with PPA on Ubuntu.)