The marketing men will have you believe because extended chokes are longer, they therefore have a more gradual taper and / or a longer parallel section which is meant to help stabilise the shot better than the shorter flush chokes.
Having owned Teague flush and OEM extended for a Beretta I spent a bit of time testing to see if I was disadvantaged, I can safely say I couldn’t tell any difference in performance.
The marketing men again say ported chokes are meant to reduce muzzle flip, or strip the wad from the shot. I bought some Briley ported chokes in the past to try and reduce the weight of the ridiculously heavy Midas chokes in a Browning. They did weigh less but I certainly didn’t notice any reduction in flip or magical wad striping, but I did notice the unholy mess and gunk between the top and bottom choke.
I would only buy ported chokes again on pain of death or a sponsorship that involved someone else cleaning my gun.
Having owned both Teauge and Briley I can say get whatever floats your boat, both are well made, neither outperform any other choke like for like (based on actual measured constriction not what is marked on the side as the manufacture’s interpretation of that constriction).
I will say Briley’s marketing department are, let’s say, more inventive in their claims.