A consideration that may favor the 6x7 over the 6x6 is that you can crop the 6x7 to 6x6 and keep the area of the negative that's left in its original size, but making a rectangle out of the square makes the 6x6 into a 6x4.5 or so.
That argument is usually used for favoring 645 over 6x6 (as in, once you crop a 6x6 down for a 8x10 print it's the same negative area as a 645).
But I think it's an urban myth.
We all crop, no matter what we shoot. We crop 35 mm negatives, we crop 6x6 negatives and we certainly crop 6x7 negatives.
There are some purists who insist on printing full-frame but they are definitely the minority, cropping is both an aesthetic and compositional decision.
So don't think that 645 is more practical because you never have to crop. And don't think 6x6 is dumb because you always have to crop.
Indeed, the advantage of 6x6 is that you can crop either way.
As for the Mamiya 67 vs Hassy, image quality differences are trivial unless you print 6' sized prints. Make a decision based on cost, ergonomics, etc.