I know this is an old post but my answer still applies today, so I thought I would share...
R and U versions in the ASUS router only offers really subtle differences in terms of network standards such as IEEE802.11.. etc. In most cases, the R versions were sold only through certain brick and mortar stores like Best Buy and Walmart. Online retailers like Ebay and Amazon have now picked up both variants as used and refurbished models are out there now. So online now you will see both variants.
The R and U lineup typically have identical performance specifications with the exception of the network standards, (the R's offering wider network standards). R and U units with the same pre-fix to a basic router user are pretty much identical and buying the cheaper of what's available would be the best bet. As you are probably not likely going to see a difference between the two in performance.
The nuts and bolts of it for the RT-AC66 series is that the RT-AC66R has additional network standards, which the RT-AC66U doesn't have, it supports IEEE802.11D, IEEE802.3, IEEE802.11I, IEEE802.11E. Also the RT-AC66U uses a frequency of either 2.4GHz or 5GHz, where the RT-AC66R uses a variable frequency between 2.4GHz~2.4835GHz and 5.1GHz~5.8GHz.
Hope this helps and doesn't serve to confuse more!