I just looked through an SRO for the first time at the SCI show last week. It is really amazing from a clarity standpoint and I did like the larger window. Pricey but really sweet. Personally I liked it better than the RMR based on looking through both. The window on the RMR just seems tiny after you look through the SRO.
Ive not owned an RMR so cant comment beyond a couple friends who really like them. I own two FF3s, an FF2 and a Nikon Spur and they all have been excellent on my 12 ga SBE and magnum revolver set ups. The FF3 is half the price and more than durable enough for turkey applications. Ive been running one for years with zero issues other than losing a couple dust covers along the way. For a turkey gun and if it were RMR vs FF3, assuming equal durability, similar window size, and perhaps easier battery changes on FF3? Id be inclined to go FF3 and save the money. No vortex experience so wont opine.
Burris just announced the FF4 which I was able to look through at the same show. New dust cover arrangement but the big news is they will have a built in choice of reticles you can change easily. 3MOA dot and circle dot which I really liked. Prior to learning this I had just bought a Holosun 507A, mainly to get the reticle options. Waiting for a Sumtoy mount for that now for a new M2 20 gauge. It has a bit larger window than the burris units and RMR and some options I liked. Will see how it does. Lots of reflex site options out there all of a sudden.