No, the difference is more due to the different shapes and the EVO 70 is definitely a much bigger feeling board than those two.
It's hard to say how you will fins the EVO 62. Some never notice that it is not an upwind rocket while others do. If your Quatro is not an unusually fast version, I think you will for sure find the EVO 62 much easier upwind. But again, the PA68 is an upwind rocket, so if that's the priority then the PA68 is surely the right board.
The EVO 62 does not only turn better over the back foot. It turns more overall.