I sound like a broken record, but you're asking for the best shoe for disc golf. Sooooo without a doubt It's the 5-10 AKA: Five Ten brand. I have had a pair of 5-10 Impact high tops going on three years now and have two more as backups. The toe area is starting to wear, but not wear through yet. They make several styles. The Impacts are made for downhill mountain biking. So they are very thick and rigid at 1st. Don't let the looks fool you (Vans on roids) They are far from that! The Stealth rubber is nice and tacky, but for some reason they don't wear out that fast. I took these up to WA and OR for a junket. It was like I was throwing from dry teepads. No slipping at all!!They are also great for rocky surfaces do to the thick padding on the high top portion.
They also have some trail/hiking looking shoes. I say "looking", because the are for approach or base climbing. All their shoes are very stiff at first, but that changes after a bit. Heck, going on three years and they fit and feel very comfy.
FOR ME! They are without a doubt the BEST shoes I've tried for disc golf and that is a long list : Merrill, Montrail, Vasque, Oboz, Ahuna, Keen (Should stick to clogs!), NB, Asics, Nike etc..... Man, people have to try these shoes. Chances are that you'de buy no other brand after you give them a try.
Now after ranting about them. 1: I don't work for them
and 2: These are the BEST shoe's that ME, MYSELF, and I have owned for playing.
Good luck shoe shopping!