I sort of have the best of both worlds. My graded cards are all in boxes, but since I've scanned the front and backs of each and created digital albums (thanks PSA!), I can view them anytime I want from the comfort of .... well, anywhere.
My as-God-intended-them-to-be cards are in binders (front and back visible), so those are easy to leaf through as well, but I don't tend to since that would require me getting up from my comfortable place.
