I have played both games, and I prefer WAR.
They 2 biggest differences are the aesthetics of the games and how the "end game" plays out.
Aesthetics-wise WAR is darker and grittier than WOW. To give a video game analogy, WAR looks the way I'd imagine a Diablo mmo would look like if it had to maintain a Teen rating.
End game-wise, WAR is much more focused on PVP, rather than instance raids. There is no big boss that both sides are trying to defeat in WAR, instead the end is focused on fighting to control the pvp areas to attempt to raise the other sides capitol.
As for the cheers and jeers...
WOW has a much more refined crafting system. WAR's system is anemic at best.
The Public Quests in WAR are a nice addition that are kind of their version of the instances in WOW. In various areas in the world there are boss battles that can be triggered by achieving certain goals, such as killing 75 mobs of a certain type within that area. Once that threshold is reached, you may have to kill 10 or so champion level mobs that appear within a certain time frame. Once that is complete a hero or lord level boss will appear. These PQ's are not instances, just hidden out there in the game world, anyone going by can join in at any time. Once the boss is dead a loot chest will drop and those that contribute the most have a chance to get some good gear.
WAR's open party system is also a nice addition, when you create a party you have the option of making it open. This means that anyone else can bring up a party list a get a list of parties they can join, showing what they are doing (PVE, PVP, or PQs) and how far away they are. This can be very useful both in PVP and in doing PQs.
The other little thing that is nice is the fact that you have both a friendly and enemy target in WAR, so if you are a healer, you have have an enemy target that your attack will go against and a friendly that your heals go towards.