Participation in the peer review process as a reviewer can indeed feel extremely rewarding or extremely time-consuming and thankless, and everything in between.
In my personal experience, honestly I think I have felt the greatest "reward" when (a) the manuscript I was asked to review seemed interesting and quality in the first place and (b) I was able to see it improved and on to successful publication in the appropriate place. Obviously this is a bit circular, and surely it shouldn't only feel rewarding to serve as a reviewer when the paper is already good and bound for publication from the start. But again, the times I think of when reviewing has felt tedioius and least rewarding are when the paper pretty clearly is not up to the standards of the journal in question and I feel I'm simply being asked to spend my time just validating what the editors probably already know - that they will decline to publish it.
In identifying this though, I can see that even in the latter cases there is some room to feel like I'm helping - by suggesting areas the paper could be improved, or sometimes by explicitly suggesting more appropriate journals that the author might try submitting to instead (journal-fit is something I'm pretty interested in, so I enjoy that). Regarding the sort of rewards you identified in writing groups Brian, I have to say I don't think I've EVER received specific feedback (positive or negative) on the actual quality of my comments from an editor or an author during peer review for a journal, but I do definitely appreciate this during informal reviewing for friends and colleagues, and I could see that making it feel more rewarding for a journal.
I also like reviewing for a journal that I'm specifically interested in topically (e.g. a specialty journal, perhaps in a field I'm interested in being a contributing and respected 'part' of). Finally, to some small degree, I suppose one could say that it's "rewarding" in a base sense simply to be able to add 'reviewed for X, Y, and Z journals' to one's CV. This isn't very good for the journal though, as it suggests no cumulative reward for reviewing for the same journal again...
Interestingly, my basic feelings about this apparently seem to match decently with what other reviewers say. According to this 2008 study (see pp. 8-9), most reviewers say they do so for 'altruistic' reasons (including being able to improve a paper and be part of a community), and less for their own gain. However, when material rewards are offered, it DOES apparently increase a prospective reviewer's likelihood of agreeing to review! These are things I've never even thought about (I'd never even heard of reveiwers getting anything for their work in my field, ha ha), so perhaps worth quoting:
"From the reviewers’ perspective, the incentives they said were most likely to encourage them to act for a journal were:
- a free subscription to the journal (56% said this would make them more likely to review forthe journal)
- acknowledgement in the journal (44%)
- payment in kind by the journal, for example waiver of colour or other publication charges, free offprints, etc. (43%).
"Reviewers were divided on whetherthey should be paid for each review they completed: 35% agreed that they should, while 40% disagreed. Those from the Anglophone regions were the most opposed to payment, whereas researchers from Asia and from Europe were on balance just in favour (44% for, 32% against)."
I have to admit I would totally be more likely to review for a journal if it got me a free subscription.
In sum though, that study finds that "For the most part, respondents’ views on these questions appear to be personal matters, independent of their field of research." Huh.