I own neither a mini-qj or a mefferts one. I'm only going on word of mouth.
I have also heard that mini QJ's are better than normal ones and that Mefferts are better still. I can't really say for certain.
What I can say is that I am very impressed with my regular QJ. I paid $9.90 from Deal Extreme, inc shipping. It took a while to arrive, but then again, so has everything I ever ordered from Mefferts.
The QJ is a clone of a Mefferts. I hear that the Mefferts one is better because it's slightly higher quality. Some people have complained that the QJs have broken. This has not happened to me yet (fingers crossed). The Mefferts one does cost a lot more ($18 inc shipping).
The Eastsheen is about the same cost as the QJ, and is far more stable and robust. Mine have never popped or broken. It is very prone to lockups, however, so is not a good speedcube. It is good for beginners though.
Please take off topic discussion off this forum. Thanks.