Babel tower tile #15 (ignore resource cost for Wonder) overpowered?
You have played correctly; tile #15 indeed lets you construct wonder stages without paying the resource cost. It's very true that some Wonders will benefit much more: Gizah B, with its massive 4 stages, will be able to take 20 points for "free" (using 4 actions), even if other players conspire to lock this player out of resources, which is very possible in 3-player or 7-player games. On the other hand, Rhodes B would benefit little, with only 2 stages to construct.

Furthermore, your feelings are justified; yes each Babel tile tilts the game to one way or another. They are not meant to be "fair for all". However, in general you may find both tiles that tilt the game to either way; take for example the opposite tile, tile #16: every player will have to pay a tax for each wonder stage; Gizah B would effectively have to pay 10 coins (+ any resources, if applicable) to construct all wonder stages. In another example, tile #22 double the penalty for losing a Military battle, while tile #19 diminishes the points gained by the victors, making military less or more important, respectively.

Finally, if you feel that one tile turns "god mode" on for a specific player, there's always a solution: conspire with other players to cover the tile. If you do it correctly, it won't stay there for more than a single turn.