So far it has been a PvP for PvP sake except for AV, when johnny PvE starts running WSG for that "leet blue swoard" reward you'll begin to see the factions do in fact differ... "quantifiably". Alliance has always been the worse in that.
They have not always been worse in that, at least not significantly.
There used to be a website where you could see a breakdown of wins and losses on all servers, in all battlegroups, across specific bgs and all BGs combined. This is about as close as you can come to quantifying the historic skill of each faction independently. Hell if I know where it is now, or if it even still exists. All I could find now when looking for it was this post:
https://www.mmo-champion.com/threads/1586951-Dispelling-a-Myth-–-Battleground-Win-Rates
Anyway, that post seems to summarize the data that I remember looking at. The overall winning % for each faction, across all BGs, is basically dead even. 52% Horde 48% Allies in the US, and 50/50 in the EU. So lets make an argument that Horde is significantly BETTER at PVP than Alliance, to a degree over and above what can be attributable to how the game, factions and classes are actually structured.
The overall numbers do not show any significant difference between the two. Lets focus on the 3 vanilla BGs: WSG, AV, and AB.
In Vanilla/classic, the most closely mirrored BG is WSG. Historically, WSG is essentially dead even (52-48 in favor of Horde). This *could* be evidence that horde is better at PVP, sure...but it could also be evidence of a structural imbalance between the two sides. Example: 1) Shamans being more offense oriented than paladins, and 2) Will of the Forsaken being a superior racial for pvp. Regardless though, this one is pretty damned close to even. Not really a compelling argument either way TBH.
AV is the single least mirrored BG in WoW. Historically, AV favors Alliance and it's not even remotely close (85% win ratio). This *could* be a counter argument, showing conclusively that Alliance is better at pvp than horde is. It could also be a compelling argument that Alliance is better at PVE without respect to either side's ability at PVP, as this BG can be won (and often is) without any actual PVP occurring. It could also support a counter argument due to the structure of the BG itself not being anywhere remotely mirrored. Both sides have atvantages, but they are extremely different. Horde's major advantage is really that Iceblood is by far the easiest map chokepoint to defend. Alliance's main advantage is that Horde cant run past and skip engaging NPCs in the Ally base. A great argument can be made here that both sides have very similarly focused players in that they want to min/max their honor/rep gains, so they want the quick games: and quick games in AV structurally favor Alliance. So even though this example would seem to be a great argument AGAINST your thesis, I'm not going to make it. My conclusion from AV is that the players' skill is very similar, even though the end result is horribly, demonstrably lopsided. The only way we'd really be able to make an apt comparison would be if Blizzard had decided to rotate flip starting points between the sides: I.E. each side starts half the games on one side of the map, the other half in the other. They've never done that, never will do that, so there's no control to the comparison*.
Lastly that leaves us with a final Classic BG: Arathi Basin. It aint in classic yet, but it's a vanilla and we have now expanded to "always been worse" as a subject. AB isnt an exact mirror, but it's pretty damned close. The biggest structural advantage, IMO, is simply that it's easier to defend the lumber mill, farm and blacksmith than any other combination of flags on the map...and this gives the horde a significant advantage if true. Regardless: this is the map that gives you the best argument of the three as it historically favors horde to a non trivial degree (I.E. horde wins 20% more frequently than Alliance). Now my response to that would simply be that once you account for structural advantages (map layout, gear, racials, class disparity, etc...which mostly favors Horde), the existence of any difference in the median skill level of the playerbase per side is negligible.
The main difference I see in classic as it is today, though, is just raw numbers. The secondary difference I've seen is group composition: Horde queues in this bracket are heavy on burst, Alliance queues in this bracket are heavy on defense. Considering this common comp difference, the common alliance strategy of turtling in their base makes sense...when they have a druid that can solo snipe at the flag (which they generally have). it's a good strat, and the players become accustomed to playing that way. But a well geared Shaman...which Horde generally has... gets close to the turtled FC and gets a couple of good random rolls, the FC is toast. If a well geared & mediocre or better skilled Rogue with all cooldowns (and no concerns about saving any) ...which the horde always has... opens on the FC, he's toast in 3 seconds.
So there, I just created a wall of text arguing with myself, resulting in a conclusive maybe. Four years of night lawschool finally paid off.
* there is ONE battleground where Bliz actually did swap sides: Strand of the Ancients. The one battleground that was pretty much universally hated, and is 100% completely mirrored in structure. Horde has a massive win advantage in this one (84% win rate). This is either proof of horde's pvp dominance, or a straight up anomaly.
