I have a sample size of 1000's for most BG's.
from around 1800 combined IOC and AV battles, I've won a little over 1/4 of them as Horde.
Other BG's are closer to 50/50 with horde narrowly edging some like AB and WSG by about 55% to 45%.
Here's actual data on BG win rates for people interested in reality and not just talking out their ass based on limited personal experience:
Win rates outside AV/IoC are something like 60-40 in favour of Horde, whereas AV and IoC are 80-20 or more in favour of Alliance.
Pre-blacklisting the rates were close to 50-50 across all BGs.
The change was caused by the introduction of blacklisting. Because of the (false) perception that Alliance have an advantage in AV and IoC the vast majority of Horde players who know anything about PVP blacklist them. Conversely smart Alliance players never blacklist them. This means that on average the skill level of Alliance players in those BGs is far higher than Horde - which means Alliance mostly win, which contributes to the perception that the Alliance have an actual advantage there and more Horde players blacklist them. Negative feedback loop.
Similarly the non-AV and IoC BGs have marginally higher skill level towards Horde side therefore a higher Horde win rate.
You know what the best way for alliance to get honor gear? Do heroics. Yes I'm serious. The fastest way for alliance to get honor pvp gear, without it being AV weekend, is to do heroics and convert. It's way faster even with the loss on converting. My win rate is abysmal as alliance, the truth is. The few good alliance didn't boycott randoms, they went horde. Like everyone else. I've know a lot of high end horde pvpers that faction swapped for que times. They said the que times wasn't worth this and switched back to horde. They said they'd much rather sit in queue for 25 mins then be alliance. The rate was horrid and people were bad, and horde was just way too dominant.