Such polls in the forums, like the petitions or whatever are never representative. Relic can easily judge the strength of the factions by evaluating the data they get (split into low / mid / high / pro ELO levels) and then probably just ask a few players they know as reliable / unbiased. That should give a vastly better result
I really don't know how they balance the game but there is stats provided by someone on official board (top200).
And according to this stats, the only more or less balanced game mode is 1v1 (pre-patch), just soviet a bit a head but because those stats are made from the top 200, and well a good micro sniper is a good advantage that's it.
But all teams games are totally dominated by Axis.
And almost everyone know why, best cost effective units, strongest, less micro dependent, no weird tiers, better synergies etc.