Some doubts are the same (word choice! sentence structure!) and some differ. Often, it's also, "do I get the message across" and sometimes, "does this premise even work for these characters". And with my unpublished epic, it's "no one will care past three parts!"

I'd say that for me, because I write shorts, generally I have the same doubts, although some are stronger on one story than on the other. I'm currently thinking about something I want to write and actually wondering if I'm not letting my own issues cloud my judgement, and that one's new so... yeah, different and the same, I guess.