My question is what is the difference or benefits of a hinged bottom
door vs. a slide out door?

The slide: one handed, pull it open and there the stuff is. The drawer is
actually a LARGE basket which has a top "drawer" (where the ice maker
is)inside
the slide that can be rolled back inside to acccess what may be below in the
bigger part..

You can often just pull it out maybe 6-12" to grab what you keep handy in
the top drawer (or ice cubes), then shove it closed with your leg (no hands)

The swing open type: IIRC you have to pull the door open 90 degrees to be
able to get at the pullout rack(s) if it has any

Also, do you pack your items flat or on their side to see what's in the
freezer?

Whichever way you like..when the drawer rolls out, you can see everything
thru the sides front of the basket.