A large fish in a 40 gallon with an owner who does daily 50% water changes may be better off than one that's in a 125 gallon with an owner who does water changes once a week. But, at the end of the day, neither enclosure would ever measure up to what they would have in the wild.
So yes, a 6' tank would be slightly better for a fish than a 4' tank because a larger body of water tends to make for a more stable environment, but the real difference maker will always be water quality and frequency of water changes/replacement of old water in the tank when you're talking about these glass cages.
You could pull off an oscar in a 40 breeder, they aren't open water fish, but it would require a lot more work than an oscar in a 125+ if you want to keep it in top shape. Bigger is always better in terms of maintenance but it's not absolutely necessary.
But if you're talking something like an Umbee or any fish that is in constant motion/an open water fish, you need to go as big as you can afford. So if you can't go 8' for a full grown umbee, don't get one. If you can't go 10' for a full grown arowana (you need extra space if they spook), don't get one if you care about keeping it healthy and as safely as you can.