It all depends on what you are shooting. Meaning the type of matches you are shooting. It also depends on whether you want to be competitive.
I used to use Teflon patching when I was shooting Buffalo matches at the Western Nationals. It wasn't just the top Crossticks shooters that were using the Teflon patching, it was all of them.
The reason for this is shot to shot consistency. The reason for wiping between shots was also so you could get the ball down the bore. After all a good patch ball combo had to be started with a small hammer.
Like Smiley Grouch said you get smaller groups with the Teflon.
I used to use Texas patching, I really liked that stuff. They went out of business, so I started using Minute man patching. I did not like that as much.
I have a chunk gun that when I first made it, I worked up my loads using Texas patching.
At any rate I decided that since I didn't like what Teflon patching that was available, I would experiment with other types of patching. I was getting decent groups at 60 yards with pillow ticking with bear oil. But I never could get the groups out of that Douglass barrel that I could get with the Teflon. On the few chunk gun or crossticks matches that I shoot with it now, I use Teflon. Only gun I use it with.