Why would I choose to use Groovy when I could use Jython or Jruby? Does the language provide any inherent advantages to make up for the fact that Jython and Jruby skills are app
I would say if you need to mix Java with Jruby/Groovy, go with Groovy. As everybody said, Groovy has tighter Java integration.
But as far as the language implementation goes, I prefer the Ruby language over Groovy, the language revolves around itself, in Groovy there are some hacks that are inherent to the implementation itself (just watch a Grails stacktrace vs. a Rails stacktrace and you'll see what I mean).
I highly recommend seeing Neal Ford's comparison of Groovy and JRuby