So which project should you choose? ThreeTen-Backport or Joda-Time?
Date and Time libarary pre-Java 8
Over the years, I have produced two libraries for Java date and time.
The first is Joda-Time, a library has become the de facto standard choice for many users.
The second is JSR-310, included as java.time in Java SE 8. Today I released v1.0 of ThreeTen-Backport, which makes the same JSR-310 API available in Java SE 6 and 7, although it is under a different package name.
So which should you choose?
If you are on Java SE 8 then you should use java.time (JSR-310). It tackles many issues with Joda-Time and is better integrated with the rest of the Java core libraries. Where necessary, consider using ThreeTen-Extra for any additional functionality that isn't in the JDK.
If you are on Java SE 6 or 7, then in general you should use Joda-Time. It is the standard option that other teams will be using, and it will be easier to interoperate if you stick to using Joda-Time.
The main use case for ThreeTen-Backport is if your team is using Java SE 6 or 7 but you are planning on moving to Java SE 8 in the near future. In this case, using the backport can smooth your future migration. However it will still require a package rename for your API users.
Another use case for the backport is to assist with backporting other Java SE 8 code to Java SE 7. See the retrolambda project (which could use ThreeTen-Backport but doesn't).
I hope that helps you to decide!