What effect does the type of decking used have on the stiffness of the structure?
It's difficult question to answer because there are many variables. Among them:

Composite decking material
Wood type
Wood treatment
Wood age
Climate and sun exposure

The particular brand of composite decking can dramatically affect stiffness. The early recycled plastic decking was as floppy as a noodle, especially when warmed in the sun. Later products became so hard that you had no choice but to countersink for every screw or they'd strip out in the joist.
As I mentioned, sun exposure is a factor. The difference in stiffness at 50 degrees (morning shade) and say 100 degrees (afternoon sun) is profound. Which are we considering here?
Then, what's the control decking? New pressure-treated SPF decking is quite flexible, but heavy. Those traits counter each other somewhat in terms of walking feel, but if we focus on flex, new PT decking may actually be less stiff than composites. That all changes as it dries and ages, though, and again when it begins to degrade after a decade or so. Cedar tends to start soft and flexible and stiffen only slightly with age. Redwood is so rare and expensive that I'll disregard it. What about teak and other &quot;exotic&quot; wood? They may be harder and stiffer.
Here's a rough ranking, in order of increasing stiffness. It's about the best I can offer.

Aged, dried 5/4 exotic (harder) wood
Aged, dried 5/4 PT SPF
Harder composites in the cool shade
Aged, dried cedar
Softer composites in the cool shade
Harder composites in the warm sun
New cedar
New PT SPF
Softer composites in the warm sun
Decaying wood