its all about the pixels. I scrap 12 x 12, 200 ppi is 2400 x 2400 pixels.
200 pixels per inch
x 12 inches
= 2400 pixels
If you resize to 7.75 x 7.75, you still have 2400 pixels, but now its roughly 310 ppi (8 x 8 would be 300 ppi exactly)
You aren't going to loose any quality going down, because your ppi becomes larger. going up on the other hand could cause some loss of quality because you will have less pixels per inch.
200 pixels per inch
x 8 inches
= 1600 pixels
by resizing to 12 x 12 you now have the same 1600 pixels, but more inches means fewer ppi, this would be appx 134 ppi.
this is the main reason why I scrap 12 x 12. I don't think I would ever have a need to go larger, but I might want to go smaller.
This is how I understand it, but maybe someone else can give a different POV