I'm 6'5" ~200lbs and ride a B17 on one bike (plus C17 on others) and have had the opportunity to compare with two sprung models, just not a Flyer.
First was a Brooks Conquest (which I think is more like a sprung Brooks Pro.) Second is a vintage B72 double or 4 railed saddle with a different spring design than the Flyer or Conquest.
As already mentioned regarding weight, the greatest difference I noticed was the weight of the Conquest vs. the B17. This was more pronounced on a light single speed road bike that I installed it when wanting to soften some of the local terrain when using this as an all around bike. I didn't notice it so much when riding but when wheeling the bike around the home it was noticeable and made this light single speed build feel oddly top heavy, not in such a bad way that it was an issue, but noticeable. The saddle otherwise did what I hoped and at my weight I did feel the springs function on rougher terrain but if/when I flipped the wheel to ride fixed and had to spin at any point then it did become more noticeable with it's springiness and less desireable movement at those times. Ultimately, it was this fixed induced spinning springiness and the overall narrowness of the Conquest shape that made me go a different direction and I eventually traded or sold it opportunistically when it was a model being sought by another member here or iBob.
The other difference to note will be a change in seatpost positioning due to the taller saddle frame. As long as you have some room to adjust the post down a bit to compensate and are prepared to tweak nose angle and fore/aft. Obviously relevant for any saddle swap and not likely an issue unless you happen to have a certain type of post with limited adjustment range and an tall fitting frame - i.e. an already slammed post!
B72 is a completely different discussion so won't go into it much here but I still have the saddle and ended up decommissioning it based in it's age and wear but I definitely noticed the spring movement when using it and have considered an eventual replacement now that Brooks has reissued it just do not have the immediate need and enjoying the B17 and C17 currently in use on my existing bikes.
Brian in NJ