I like the first version better, but I do like the final line of the second.

Other thoughts:
“refuse to take sides” > “refuse to take a side”
“the Council of Neutral Systems” > “a COUNCIL OF NEUTRAL SYSTEMS”
“to preserve their peace” > “to preserve the peace” (but is it really even “preserving” at this point?)

I definitely don’t like “after destroying his flagship.” If you want the context in version 2, maybe use “With the Malevolence destroyed, the clone army hunts for Grievous, while Anakin returns Ahsoka to the Jedi temple to continue her studies.”

Is there room to change “Now” to “Meanwhile?” But then it might sound too much like the “while” in the prior sentence.

Should the Attack on the Republic cruiser be shown briefly at the start of the episode, much like the battle with the Malevolence was shown at the start of the prior episode? Or would that be creating too much of a pattern, where something happens, then we go investigate it?