So I went on a great premium denim trying-on spree last weekend, and here's what I found. I have a larger waist relative to my hips and thighs (apple-y), and I much much much prefer a low rise, since it doesn't make me look like I'm wearing a diaper (my tummy isn't quite big enough that I'm really so concerned with the "lock and load" effect of a mid-rise or high rise), so I ended up with two pairs of Hudsons. My waist measurement is something like 27" and my hip measurement hovers around or just under 36"--I usually take a 4 in American Eagle or Gap jeans, although recently I've gone as low as a 2. I tried on Joe's (rocker and some other cuts--the low rise ones looked way better), and the 27s seemed the closest to the right size, but I could squeeze into the 26s, and if I were getting a wash I knew loosened up, I would've gone for the 26s. In the end, I ended up getting 2 pairs of Hudsons in a 26--the 27s looked like a better fit, but I could definitely get the 26s on and they looked good, just tighter, but apparently that's what you're looking for with these kinds of jeans.
All of which is to say that I took a 26 in Hudson, a 26 or a 27 in Joe's, and a decided 27 in COH (Kelly, Ingrid, and whatever the petite fit is called). The 26s in COH were a non-starter. Too tight; did not look good. Whereas there is a pair of Ingrids in a 27 (a fairly rigid fabric) at my local consignment store that I've tried on twice and look super-cute, but I just can't bite the bullet. But that's definitely the right size in that style and wash.
(I was also definitely a 27 and not a 26 in Paige, if that helps. Possibly trending into a 28, if I remember correctly. I think I was also mostly a 27 in 7FAM, but none were low-rise enough and they all looked like crap.)
So I would say that COHs run a smidge smaller than Joe's, and a little smaller than Hudson. However, this could be because of the styles I tried on (all bootcuts), so I can't speak for the Avedon directly. But I just went and had a gander at the sizing charts on Nordstrom.com, and they seemed to match up with my memory of the sizes that did and didn't work for me across brands. I think Revolve also has fit notes for COH.