Both designs as shown would need 2 screws on the X.. Both could also be modified (longer uprights/sides for the gantry, extending below the bed) for a single screw.
Design 2 is easier to make the gantry stiff. The Uprights and the connection to the gantry are typically your weakest point, especially when using wood, so you would need substantial re-inforcement there.
By taking out the uprights, you remove that weak part and your gantry can withstand much higher forces.
Another advantage for Design 2 is that you create a natural enclosure that will help to keep dust to a minimum while also providing a 'safety-wall' when for example you break a bit. Very easy to add a plexiglass or wood 'door' at the front and back to make it completely enclosed.
Design 2 would also allow for a wider gantry outside of the walls, so you could make your Z-axis carriage wider, which makes it stronger to withstand cutting forces.
I've seen video of a 5 axis which is a taller version of #2 with a trunnion for A and C axes. It was pretty p0rnstar. I'm waiting to see the downside but, after all, if it there isn't a downside then why does every man and his dog (commercial machines included) tend to go for #1 ??