I've been using Asus almost exclusively for roughly a decade. My initial reason for doing so was the fact that they continued to support ECC on their consumer AMD motherboards while other vendors did not.
Linux compatibility out-of-box has been so-so, but all issues I've encountered have been solvable. Ubuntu 10.04 had problems with the NIC, audio, and temperature/fan monitoring on the Asus M5A97 EVO; all issues were addressed via use of out-of-tree drivers, and with 12.04/14.04 everything "just works". Getting Linux to boot from a software RAID-1 array on the Asus M5A97 R2.0 was a pretty major PITA, but some of that came down to my own lack of familiarity with UEFI and GPT.
The fact that AMD hasn't released a new chipset for Socket AM3+ in a very long time actually has a silver lining for Linux users -- it means their chipset driver support in current distros is mature and stable.
I have no first-hand info about their Intel boards either, as I haven't built an Intel-based system since the age of the dinosaurs. A former co-worker built an Intel-based Debian system on an Asus motherboard a couple of years ago though, and I don't recall him having any real issues aside from the same audio codec problem I hit with the M5A97 EVO and Ubuntu 10.04.