I don't think I make a difference between old and new finished stories. I try to leave at least kudos when I bookmark a story after I read it, but I don't comment on AO3 as much as I did on LJ. In part it is simply because on LJ when I commented I got the comment with the story mailed to me (I had a paid account back then) to not loose fanfic I read, so that took care of saving the story into my (searchable gmail). On AO3 downloading is that step and more convenient for me, because now I just organize them as ebooks with the tags attached.

If it is a story that posts in a few huge chunks, and the author says it is five parts or whatever, I'm likely to just wait until it is finished. Reading of actual WIPs which I also enjoy is often more interactive for me, you comment as the author is writing it, and I often have an easier time to say something, like along the lines of "that was an evil cliffhanger to leave him dangling from a helicopter" or "I hope X happens" or such.