I doubt if there would be much if any difference in image quality.
Size and weight would be enough for me, it becomes a whole new world of portability.
But you could probably add two years newer (X1D) or 4 years newer for the X1DII, which is a current model and possibly cheaper!
I can't think of any reasons to prefer the H5 other than if you need to use it on a tech camera, or want a waist level finder.
The EVF is the main difference. You can't just look through the view finder. The camera has to be on for a start.
Annoying at first but you soon get used to it and I love the ability to see in the almost dark.
I loved my 4 of H series cameras, but the H series now is a virtual steam engine with lots of moving parts. None in the X1D except the wheels.
Haven't you had both of these cameras?