From their own benchmarks it seems more like bzip3 is geared towards a different compression/speed trade-off than bzip2, rather than an unambiguous all-around improvement. Am I misreading it?
edit: ah, bzip3 is parallelizable, while bzip2 isn't. That alone is enough for me to be able to claim 'faster'.
In practice it works, but it isn't pretty ;)
(context: I have had a situation where files created by pbzip2 on linux were not able to be decompressed with some library on .NET, but using lbzip2, they were. I never looked into the details.)