I will share my own listening experience but since they are largely based on sonic memory, please take them with a grain of salt.
I last listened to the UERM demo more than a year ago, I last listened to my own NT6 more than 4 months ago after putting it up for sale, and I listened to the UERR last week.
In Q4 2014, I was deciding between the UERM and NT6 having found both to be close to my desired sound signature. I ultimately chose the NT6 over the UERM because the UERM is really neutral, resulting in the sound being a little harsh, and the body thin. The NT6 is slightly more full bodied and has greater bass presence (but still bass light).
The UERR is much more enjoyable compared to the two, with the harshness gone, and sound much more full bodied compared to the two, but the neutral and uncolored sound signature as well as clarity is retained. The UERR is on my "to buy" list, after the FS MG6Pro.
Another customs that you can consider if you desire a neutral sound is the Hum Pristine Reference. It's not ruler flat, as it has a greater and enjoyable bass presence, while the sound is very slightly colored, but it's probably more enjoyable to a larger audience who I find to prefer a warmer and fuller-bodied sound.