I think it should be private, if done at all. It also depends on how in depth the critique is going to be.

On the one hand, criticism is never a bad thing so long as it's constructive and given with the best of intentions. On the other hand, criticism is also incredibly subjective and while one person's opinion may be valuable to some, other people may completely disagree [with it] and not appreciate getting it without asking for it tin the first place.
This isn't a competition where the authors submitted their work, thus giving the admins free reign to do whatsoever they choose. The fics were largely nominated by fans/readers of the nominated authors. Many authors don't even know they were nominated. I didn't until a reader told me she had.
And while I respect all opinions, unless it's asked for, I wouldn't want a critique of my fic/s because as much as I value opinions, my opinion is the one that counts the most. I write for myself as much as I write for my readers so if I'm satisfied, if the authors are satisfied, I don't think a review is necessary.

That being said, if an author specifically asks for a critique, have at it. I know that there are people here who do need and want feedback from more objective, knowledgeable sources.

Ask permission from author.

I can understand why people would get upset about making the reviews public but personally constructive criticism is whar writers need. Sure it gets them down in the dumps for a while but as someone who's been through that and to a certain extent STILL going through that, it makes them better writers.

Also I think readers should have the reviews to help them choose perhaps.

i think you should ask the authors first. you can put both private and public. maybe you can attach [privately review] beside the titles if the authors want it private and write the review for the authors who accept it to be public.

ask the author permission first before publishing the reviews.

i, and maybe a lot of err, family (:D) here do want to make the reviews be public, but if the authors don't feel to, then let it be private. hee

I think being nominated for this award is already an achievement for the author .I do not want to let them down by publishing the review.Just give the review privately.

AMEN, kpoppunks, AMEN.

I wish I could reply to the comment below me, but unfortunately I can't.

Amen to that, kpoppunks.

Private.

Because, as an author who was nominated a few times, I don't want my work publicly reviewed. I didn't volunteer or ask for it, so it wouldn't be fair to me. And, honestly, you could follow the popular vote and post the reviews publicly, but you've already realized that there are authors who don't want reviews of their fics to be made public, so why even risk upsetting them...?