Depends what the bias is.
Blizzard does give individual Horde characters plenty of spotlight. Thrall, Garrosh, Sylvanas, Saurfang. Alliance has had Tyrande and Anduin lately and from what I’ve gathered they aren’t the most popular characters for Ally’s so some may feel the spotlight could be better spent on others.
In terms of winning though I don’t think the Horde can claim any real “win” at anything, unless of course they’re teaming with the Alliance which cancels it out. Alliance can actually claim wins.
In terms of environment I’d say it’s fairly even until expansions with no shared city hubs. Alliance had it way better in WoD with their garrison, even you if preferred the Horde aesthetic the Horde buildings are laughably small compared to the Alliances much bigger buildings (compare the town halls). In BfA though I’d say Horde got it better, Dazar’alor is massive and such a unique and flavourful city compared to Boralus that just looks bland and a bigger version of smaller Kul’Tiran towns elsewhere.
In terms of superhero Avenger characters. Alliance wins hands down. Jaina, Malfurion, Turalyon, Alleria, Varian (not anymore), Velen & Anduin now.
Horde has… had… Thrall (not anymore), Sylvanas (not anymore), Garrosh (not anymore), Cairne (not anymore), Vol’jin (not anymore). Currently I dunno? Thalyssra? Lor’themar would be cool as a spellbreaker but he’s not, so he doesn’t count. Gazlowe would be cool if Blizz shows him more tech’d up like a Goblin Ironman. Baine is Baine. Thalyssra?
So yeah, I’d say the bias depends on what it is. I think the one thing that distinctly separates the Horde and Alliance is the Alliance has been smooth sailing, steady as she goes, hardly any change throughout the years. While the Horde has been volatile and always changing.
Blizzard definitely has a lot of love for the Horde as a faction, the way they’re treated in game though, I don’t believe there is Horde bias. I also don’t believe there is Alliance bias in game either besides Ally having the Avengers on their side and Horde has… Thalyssra?
The books is where I’d say the bias’ are, many Horde characters are written as if they were Alliance. The way they talk, act, behave. They’re just humans in costume.