Rubinius boots negligibly faster than JRuby; for simple scripts, JRuby takes around 0.5s on my system versus 0.35s for Rubinius. All implementations that JIT to get to full speed will have startup issues.
JRuby does not use any of Rubinius's standard library. We do both share most of MRI's standard library, however.
As for RubySpec; Rubinius started it, and JRuby is a very heavy contributor to the project. However JRuby also runs many other Ruby test suites, so we have not been as dependent on filling out RubySpec.
We do both share implementation ideas and advocate for each other in debates with ruby-core. Hopefully in the future we can work together on adding new standard APIs as well (rather than unilaterally adding them to one implementation or the other).
It's great to hear that the startup time has improved so much.
JRuby uses UTF-16 as its internal string encoding, so Rubinius is going to use a lot less memory. It can also boot its VM more quickly since the client hotspot JVM has been largely neglected in favour of optimizing JIT for long-running processes. I would use JRuby for sure by default, but there may be places where these two things would disqualify it.
Rubinius development also feeds into JRuby--I believe JRuby uses some of Rubinius's standard library (or at least it used to), and rubyspec came from Rubinius as well.