Does your faction matter?

I have several characters in World of Warcraft that I play most frequently, two being Horde and three being Alliance. My two Horde may well be my most frequently played at the moment, with both my warrior and shaman being active in their guild, but when my wife is home I generally play with her, and that means playing Alliance.

I don't know how or why it happened, but we've developed totally different mindsets. She is very invested in the Alliance questlines and stories, to the point where unfinished or unresolved quests annoy her, and she can't get into playing Horde with quests involving feeding diseased food and drink to helpless prisoners. As she put it when we discussed the situation, there's a world of difference between stiffing workers out of their pay and plotting to exterminate all life on Azeroth.

For myself, however, I have no trouble playing Horde. But when I'm playing my tauren or orc characters, I run into the opposite issue: many of my guildies are excellent players but they really dislike the Alliance, especially night elves. The amount of anti-NE bias I run into seriously staggers me at times. Maybe it's just because I have a night elf at 70 as well, but it always floors and baffled me when I run into statements like "All the Alliance are little kids" and "Horde players are more mature" because, well, so far I've seen utter toolboxes and jackasses in my time on both factions. The same proportion of people who teabag their dead opponents in PvP, the same general amounts of noobishness and dickery in the chat channels... I just honestly don't get why someone would prefer one over the other. Horde and Alliance both have their own compelling storylines and their own unique NPC's, and some fun quests as well as ones that ask you to do objectionable things.

I personally have no problem killing Alliance on my Horde toons or vice versa. In fact, I've often wished I could somehow PvP against myself, so to speak: I'd love to see how my tauren would fare going up against my night elf. (I suspect the tauren would win, he has much better gear and I think I've come up with a really effective build for him.) I guess for me the cross faction antagonism is just another element of the game.

What do you think? Is it important to pick a faction and support it? Does it enhance or detract from your ability to experience all the game has to offer? Or are you missing out if you're not invested in your faction?