Classic:
1) Early leveling experience was better for groupies as 3 races were funneled into Barrens while Alliance stayed separate
2) RFC dungeon is a better dungeon to have than Stockades for the Alliance
3) Because Horde races were funnelled to Barrens they had easier time forming groups for WC
4) Some quest rewards exclusive to Horde were also better like Wing Blade
5) Horde exclusive: Warchief Blessing granting 15% attack speed is a massive advantage for melee DPS which are already favoured in Classic.
Then we had few Blizzcon incidents like "have mercy" alliance warcry and Corpsegrinder trashtalking all who chose to play alliance.
I'm sure someone who bothered to remember stuff over the years could point out few more examples.