No ones asked you about the catfish... you says its large and they are naturally nighttime predators... Cats can have big mouths and i wouldnt be surprised if it couldnt fit a betta into its gob overnight as bettas tend to sleep at the bottom of the tank at lights out.
Tho i do have a story to tell about bettas and it prolly applies cos you have a Jewel tank. Bettas are surface dwellers and tend to stick to the top of the tank, however when water changing like most people you prolly take out the filter media for a quick squeeze in the old water to rid it of any debris and change the polypad that goes on the top. Well to do this you have to remove the powerhead leaving a gaping hole that the surface dwellers will see and at a 25% change is normally where the water level is during a change, and cos its dark in the juwel filter housing makes an ideal place to go lurk and get away from the rest of the busy tankmates (male bettas are naturally quite solitary fish in my opinion and tend to lurk somewhere where the water movement is real low... like inside the housing when the powerhead isnt on). They have done it to me many times and ive found them swimming in the filter housing on more than one occasion because theyve slipped into that hole when u wasnt looking. Maybe you should take a quick peek, and altho it saddens me to say it check between the media baskets too & at the very bottom of the housing underneath the filter baskets, youll prolly need a torch as its very dark in there(i assume you have 2 baskets, one for the fine sponges & one for the coarse, nitrate & carbon sponges).
Another thing, Tiger Barbs are quite pugnacious fish and to be honest shouldnt be in a tank with any fish smaller than itself, or slow moving or with long fins, ive also found Red Eye Tetras to be a little aggressive (well for Tetras they are) towards smaller fish. Everyone else has already mentioned the Angels natural diet of neons, if its a large one i guess hes more than likely the culprit of that fishes dissapearance.