There isn't the same quick and easy option. You would have to get a reference to everything styled with the orignal, apply the new one, then delete the original. This is a VERY rough and ready bit of AS that does it:
tell document 1 of application "QuarkXPress"
set to_change to object reference of text style ranges of every story whose paragraph style is "Bullets"
repeat with text_chunk in to_change
set paragraph style of text_chunk to "Highlights Base"
end repeat
end tell
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Note that this won't override any local styling (like option-clicking on a style). That can be done, you'd have to add a line to apply 'no style' I guess, but I haven't time to play with it right now!