I've always preferred to cross my tie-downs. Common sense tells me the car has less chance of shifting side-to-side in a mishap of any kind.
As far as hooking to the suspension vs the body that's a whole other can of worms. My Nova is currently in my trailer and I have the front straps hooked to the frame and the rear ones to the axle! Duh!
(actually there's a reason for it but the explanation takes too long.
)