I've been struggling with the same decision---to rest or not. I picked up a half-dozen old Flipper Rests off an auction sight -- got em all, new in the box for less than $10 including shipping. I have several Bear Weather Rests.
I received Dave's personal Lefty Silvertip around August to try out. It had a Bear Weather rest under moleskin like the picture above. I liked it and of course left it in place as I would be returning the try-out bow. I have a plunger style springy rest on my Stricklands's "Stick".
At basement range distances (13 yards) I couldn't tell any difference in my accuracy off the shelf or with an elevated rest. It was a pain however switching back on forth on the same bows as I had to cut off my tied on nock locators and re-tie so they were at the correct height. I know, I should have used brass jobs to make this quicker.
I've shot feathers and vanes off rests and the shelf. Frankly, I don't see a lot of difference with any of these set-ups. I'm thinking "paradox" keeps the vanes and feathers from contact with my shelf and window but I haven't used powder or lipstick to check it and I don't have a camera that will tell the tale.
I shoot one of my bows better than the others, most of the time. This bow doesn't fit my "purty-criteria" as it has a metal riser and is completely camouflaged. However, it is my best shooting rig. It has the elevated, plunger with springy arm. I'm sure the difference is this rest. In fact, I almost had a Silvertip that is due any day, drilled for this same rest. I chickened out at the last moment and ordered it to shoot off the shelf.
I suspect I'm going to give the elevated rest another try and shoot at further distances. I'm hopeful that I don't notice a lot of distance because 1). I'm pretty picky about arrow tuning and 2). My shooting process is well-practiced?
My best friend, who was a multiple IBO triple crown champ with recurves back before they moved the distances so close (Jim Hart in case any of you were shooting in the late 80's and 90's) swears by a flipper. He won't even consider shooting off the shelf. His rest of choice is a highly mechanical affair with springs and screws so I worry for him a bit that it could go Murphy on him someday.