The short answer is we don't know, because Jackson doesn't show us and Tolkien doesn't tell us.
We never read or see Gollum wearing the Ring in The Hobbit. And by the time of LotR, he's long lost it.
I am sure that Frodo is enjoined to never wear the Ring because by that time it's known already that Sauron is back and looking for it. No such injunction was ever made on Smeagol, nor was it needed, because Sauron was long gone at that time.
However, we can conjecture.
Jackson shows us explicitly what Frodo sees when he's wearing the Ring: he can see the Nine as bright figures, he can see their ruined faces; Aragorn appears dark. Jackson also shows us what Bilbo can see when he's wearing the Ring: he can see Thorin & Co and Gollum as well as greyish figures; during the Battle of Dale, he can see Elves as bright figures and Orcs as dark shadowy figures.
Bilbo and Frodo were both clearly good folk. Predisposed to doing what is right & good at need. Smeagol was clearly not so good a person. He was predisposed to doing whatever it takes to get what he wants, even if in very small, very mean ways. He was not above murdering his friend in order to get the Ring in the first place. While I'm sure the Ring played a crucial role at that moment, the disposition towards evil was there.
I would hazard the guess that it conferred on Smeagol a similar kind of enhanced vision. It might have allowed him to look into dark places and find secrets more easily. He'd probably see his Orckish prey as brighter shadows in the dark. It is possible that other senses were similarly enhanced.