First off, a disclaimer in large letters so I don't have to hear bitching from people who didn't read my post:
This thread is not to discuss whether or not Blizzard favors the Horde. There are already plenty of threads on that topic, and most of them just devolve into a flamefest.
I don't think it's a secret to anyone that the Alliance lacks the same pride that the Horde has. Many have argued the reasons for this, but I believe it ultimately comes down to how poorly the Alliance has been handled. I will not speculate on why they have been handled so poorly - as the disclaimer mentions, there are plenty of pointless threads that already do this. I will, instead, outline what I believe needs to happen to even the faction pride.
1. The Alliance needs more heroes, and the heroes they have need to stay Alliance.
Throughout WoW's history, many of the Alliance's best have given up their allegiance to the Alliance in order to serve the needs of Azeroth as a whole. I understand why they do this, and it can be a great plot device, but it needs to stop. If they want to make them neutral for an expansion before returning them to their proper faction - as they're doing with Thrall - that's fine, but don't take away figures central to the Alliance. Tirion dissolving the Knights of the Silver Hand to make a neutral faction would have been fine for just Wrath, but the loss of one of the first and greatest Paladins was a heavy one. Malfurion turning from his people to stop the destruction of the world is understandable, but they need him now.
2. What heroes the Alliance does have need to be more active.
Playing as the Horde, you really feel the presence of your leaders. They interact with you pretty frequently, and you see them throughout your questing career. The Alliance needs this, and I frankly see no reason why they don't already have it. I think Varian's new 'Trials' would be a perfect place to start. I'm not sure what they have in mind, but having players interacting with him in a meaningful way and actually accomplishing something could go a long, long way to improve his image and the image of the Alliance as a whole. However, that would just be the start. We really need to see this with all Alliance leaders, and probably some other 'heroes' as well.
3. Alliance NPCs need to show more pride.
Horde NPCs show pride pretty consistently, and I think it really rubs off on the players. You occasionally catch this from Alliance NPCs, but I don't feel it's frequent or zealous enough to make a big difference. Many Alliance races seem mostly concerned with their own faction or their own personal demons, which I feel doesn't really make sense. We should be seeing all races working together on all fronts, and they should all be putting their faith in the Alliance as a whole. I think seeing a Dwarf in Ashenvale fighting and dying to protect his allies could really make players feel a sense of unity.
4. The Alliance need more in-game victories (even if they're only symbolic).
The Alliance lost quite a bit in Cataclysm, and even more with the start of Mists of Pandaria. Many will argue that this was just settling the score, or that war isn't fair. While I understand the points behind these arguments, I feel they are ultimately irrelevant. Regardless of rhyme or reason, losing consistently does not feel good, and it does not inspire pride in any sense of the word. It's also a little jarring to do everything right in a quest chain and just be told that you lost after the final quest. It doesn't make for a good story, and it doesn't make for a satisfying game.
Now, this isn't to say the Alliance didn't have any major victories. The Alliance defeated the Horde army in Ashenvale pretty decisively if my understanding of the events in Wolfheart is correct. However, this wasn't seen by the vast majority of players - which, is really a shame, because I feel like it could have made a difference.
Once again, I feel like the upcoming Trials are a good place to start. Having Varian win something big over the Horde - even if it has no real bearing on the game - would be great.
5. Give the Alliance a real battle cry.
It seems trivial at first, but I believe having a catchphrase can really help. We had one going for a while with 'Glory to the Alliance', but I don't believe Blizzard kept up with it long enough for it to catch up. I propose 'By Blood and Honor' (a fairly common phrase throughout human lore), though I also believe its really irrelevant as long as Blizzard pushes it. Speaking objectively, there's nothing special about 'For the Horde', but it is said frequently enough and with enough fervor to inspire Horde players.