I have played Daoc, WoW and have been playing the WAR beta off and on for a few weeks.
I must say that WAR resembles WoW much more than it does DAoC as far as commands, and the user interface goes (which, if you played DAoC, is not entirely a bad thing...). The commands are identical, the mini-map is almost identical, the /g, /p, /s etc are all the same. They did this to make WoW players feel... at home, so to speak.
Unlike WoW, their quests are logical (I recall Kraniac complaining several years ago about how WoW's quests made no sense, and he was correct). When you are sent out to get bat wings, for instance, you get bat wings off of every bat you kill. Why? Because all bats have wings... duh! The WoW mentality of "I hope their drop ratio is good" does not exist for these types of quests because it does not need to exist.
DAoC had revolutionary PVP for its day called RVR and WoW's PVP was clearly an after thought (the BG's did not appear until almost a year after launch). The immense imbalance of racial abilities with Alliance vs Horde could not have been a mistake. Both sets of Racial abilities are very viable in PVE, but the Horde gains much more from their racials than the Alliance does from its racials in PVP.
Blizzard should have seen that problem long before it ever had the chance to arise.
RVR on the other hand is much more in depth that regular PVP is. You can PVP all you want in WoW and the community is still the same. Unlike WoW, WAR's RVR is very important to the game. Not only do you get gear, but you get specialization points to help your character out, no matter what they are wearing. If your faction controls the capture points in an area, then your faction "controls" the zone. This simply means you get xp 10% faster than the opposing faction. If you control a keep, then you have access to buy armor there. Every bit helps, and it's more help than you got in WoW.
My feeling is that WAR will not kill WoW, but instead it will impact the population of WoW that values skill over anything else and enjoys PVP over PVE. WoW was built in such a way so that a great population of people could enjoy playing it, and lets not forget that the company behind it is fairly popular with the gaming world. These are the reasons that WAR will not "kill" WoW. Blizzard did a lot of things right with WoW, Mythic is improving upon them.
Mythic is the MMO company, and well... Blizzard is still learning.