It's actually pretty easy to figure out. The Horde has been in lousy shape since the end of MoP. The Alliance was clearly WAY stronger than them at that point.
Now, fast forward to Legion and both sides got curb stomped at the Shore. They lost many of their best fighters, many temporarily, others for good. Then they decided to be idiots in Stormheim and fight each other. At this point, the Alliance is just more capable of military action. (though they can't be doing that great either)
Also, one could argue that the Light is just a more integral, core ideal in the Alliance and they are just naturally more likely to be involved in a story about it.