It's actually easier to go up that on a rigid bike. We have a nice long set of "stairs" here that you never actually pedal up just throw your body forward after getting your front wheel up. I was originally on a HT SS, I swapped forks to a rigid SS and am much faster. Most of it is made up in the efficiency on uphills and I have also enjoyed no fork compression when taking a tight turn which usually throws me off a bit. I have ridden a few full suspension bikes most of them I hated a few I really liked.

I made a silly drawing to show a route I would take.
I do not see how you could climb anything better with suspension? Most people would lock their suspension out on big climbs to make it easier. I also do not know why you would go from rigid to suspension as a progression? I can see it as a way to continue riding like a previous poster with back issues. But if you can master something on a rigid bike it would only be easier on a HT or FS.
As you can all tell I am a big support of a rigid bike and it being SS.