I'll see if I can dig up the links or posts Byron made tomorrow, but in a nutshell, fish release pheromones and allomones into the water. So a betta will release certain pheromones, and a prey fish like tetra might release allomones as a result of sensing the betta in the same waters. Have seen a video once of a certain type of sea creature, a stonefish or something maybe? Where they put it's natural predator into tank water, then removed it and placed it's prey in the same water, and the creature freaked out. It could sense the predator though hormones or chemicals or something in the water. They did a side by side of the same creature (I wish I could remember what it was!) going into clean untainted water, and going into a tank where the predator had been in the same water, and the difference was incredible, it reacted so strongly, immediately.
Things like that make me wonder whether bettas can sense another betta that's in the same water. They're so territorial, and the water they live in in the wild is often murky, it would make sense that they also use other senses to detect prey and competition. If they know another better is so close by, but can't see it and deal with it, I can imagine that leading to some chronic stress. For those reasons, I'd choose separate tanks to be on the safe side.
Thanks for bringing up this excellent point that I had not thought of! I know many people keep 2 (or more) bettas in one tank with a dvider/dividers, but I do wonder, even if the fish appears happy and healthy, if the shared water and thus pheromones does have a physical psychological effect that we simply don't notice... I have tried keeping a betta in a divided off section of a community tank before and he did not thrive until I got him his own tank, even though he could not see through the barrier, he was just never happy.
My double tail Beta is in a 5 gallon tank. Having a sole Betta in say a 30 gallon tank or 2 in a divided 75 gallon tank is overkill in my opinion. Water changes on my 5 gallon tank are EZ-PZ, taking maybe a total of 5 minutes using Orange Juice containers to remove 2 gallons of water and then refill the tank. No buckets and no Python WC is needed. A 30 gallon tank would be a waste of water and electricity for a sole beta in my opinion.
I know a lot of people would think that! And who knows, I may end up not having an obnoxiously large betta-only tank lol. At a minimum they will each be getting a 20g long, as I will have a spare one either way. But honestly I love the looks of a heavily planted blackwater tank, and I love bettas, and tank maintenance is an enjoyable part of the hobby for me, so I'm going to get them whatever size tanks I can reasonably fit in the new space.
I love my community tank, but if I really HAD to choose between a community tank or a single betta in that same size tank, I'd go with the betta. And if they are getting a larger tank, I may get some more Otos, shrimps, and snails to help justify the space lol.