As it says, the move can break something like a Screen with little trouble. Even then, I think about the only time Brick Break won't break a Screen is if the user is immensely tired or weakened and can't deliver the impact they could compared to something that's totally fresh. Additionally, a Fighting type like Mienfoo should be especially adept in using such a move, especially against a Barrier that has already took some damage. Knowing that, the Screen in this case would give way with little effort.
I hope this clears things up a bit. If you still have any questions, please don't hesitate to drop a PM/VM! You can also try asking on the Trainer and Referee Q/A on either forum.
Also, the attack description on Barrier and Reflect for examples. Ripped right from the Attack Descriptions page:
So comparatively speaking, Reflect is stronger as it blocks an Extreme amount of damage. While Barrier it weaker as is blocks a Major amount. And according to the Damage and energy terms, Extreme > Major.
If you're still wondering about Barrier, I asked about that Here and a few folks say yes. And comparatively speaking, Barrier is actually less sturdy than either Light Screen or Reflect. When a description says Major damage, yes it's alot. But it helps to bear in mind about Keywords used in Attack Descriptions. The damage/energy terms and their levels of power are found Here
You may want to note that Onix is a Level 2 Acquisition, meaning you have to make it your uplevel, or drop (Or replace) it. If you do make it one of your uplevels, however, you shall have to take uplevel status away from either Pidgeotto or Grovyle.
Also, we do not really have different stats per Pokemon in ASB. Generally, larger Pokemon are bulkier, while smaller ones are more nimble. The Species and Type characteristics would shed light on them.