The Pebble has the potential to be the generic wearable you describe. It's accelerometer and CPU are very similar to the FuelBand, and it's easy to write apps for. I'm not sure why it hasn't taken off as a sport platform. Perhaps there are software limitations or it's difficult to monetize apps.
Or perhaps there are physical constrains like the durability. On pebble's website it does mention being scratch resistant but I don't know if it can endure the frequent impact it will encounter in many sports.