My answer comes from my experience working with commercial ambulance companies, where I have used both brands of stretchers.
The Strykers are easier (in my experience) for one person to control. This is important to me because commercial ambulance companies do mostly "routine" transports, which means I push my patients through more hospital corridor in one day than most emergency unit EMTs (those responding to 911 calls and taking patients into emergency departments) walk in a week. My company is too cheap to outfit its stretchers with those parcel nets on the frame either under the head or at the bottom, which means any patient belongings (remember, this is commercial transport, meaning mostly discharges or transfers, so a lot of belongings often accumulate) have to be hand-carried, which in turn means either multiple trips in and out of the hospital, or one person carries belongings while the other controls the stretcher.
However, Strykers sometimes get jammed up on themselves. For example, my partner had dropped the back (the frame section under the head that collapses down) when our Stryker was fully raised, then lowered it with the one-man lever, and the end of the dropped frame got jammed up somehow in the bottom frame section. We didn't realize that had happened until after we had loaded the patient and I found I couldn't get the back end raised up again. Without thinking about what I was doing, I knelt down there and yanked on the dropped frame section. Unfortunately, my partner was trying to pull up on the stretcher at the same time, and had inadvertantly squeezed the drop levers, so when I freed the dropped frame section, the entire stretcher (with patient on it!) came crashing down on my head. Fortunately, the drop levers slipped out of my patients hand, so it didn't come down all the way.
I have seen this jamming up happen to several Strykers but never to a Ferno. I think it's just a matter of frame geometry.
Fernos are also lighter.
I have seen several Strykers lose fluid or gas--whatever is in the strut that holds up the head end--causing the head end to excessively bounce, which isn't very nice for the patient. I've never seen that with a Ferno.