I am probably a statisical outlier for how I interact with the site. I often do not bother to look for "newest" coments.
I use notifyhn, so: If I posted the article in question, most of the time, I will get emails notifying me of "top level" comments but not replies to them. If I commented in the discussion, most of the time, I get emails telling me oif new replies. I typically am interested in reading all of those new replies.
If I neither posted it nor commented in it, well, not all new comments are equally valuable. Stuff that floats to the top is more likely to add value. Stuff towards the bottom is often inane and does not merit more than a cursory sampling to see if the overall discussion down there is worth delving into.
I also check the new comments page a lot. If I see something intriguing there, I will click "parent" and follow it up. That has a pretty good track record.
If it is an excellent topic with an excellent discussion, assuming I have the time, I am fine with starting at the top and reading through the whole thing, even though it means rereading some stuff, in order to see comments in context.
If I really just want to see new stuff in a discussion I read portions of previoiusly, I check the time stamps. It isn't that hard if it is less than a day old. After that, time stamps get less useful.