I don't know their specific processes, but my guess is that its all in the heat treating of the finished stamp. A poorly heat treated stamp made of O1 will not hold up well, were as one that is properly heat treated for the intended purpose will.
Most of the lesser quality stamps that I've tried were also claimed to be O1, but there was a huge difference in how they performed/lasted compared to the Everstamps.
The folks at Buckeye MIGHT make a good product, but I have come to trust the quality of what Everstamp makes, and for the difference in price, the red flag goes up for me when I see a stamp, made of the same material, that costs half as much.
My philosophy is that I can pay once for a quality item, or pay many times (equaling out to, or exceeding the cost of a high quality product). Just trying to offer my experience.