no, not necessarily any better. The quality is in the metal itself not if it has HAA stamped on it or not.
I've had some with HAA on them & when i've gone to cut them my cutting blade makes an awful screeching noise & sometimes breaks! which costs me £20 to replace.
I will start to cut a customers own supplied blade but if it starts to make my machine make unhappy noises then i stop & tell them i won't cut it any further unless they're gonna replace my cutter if it snaps, or i can just supply them with a blade, which if it's just a flip blade i give it them for free