It could be one, or a combination of factors. Firstly, Smeagol was a "Stoor", one of three sub-species of hobbits that had different physical features and possibly temperaments. Stoors tended to live near rivers and such, while Frodo and Bilbo are most likely "Harfoots" which prefer hillsides to live in.There were also "Fallohides" but they don't seem to matter in this example. There is no evidence that "hobbit race" was a factor in determing resistance to the One Ring, but it is something to consider.
The rings that were given to the Elves, Dwarves and Men were made to be subservient to the One Ring that Sauron wielded and did not share the same attributes. So, as you mentioned, the Elves immediately took theirs off as soon as Sauron put his on, and they hid them.
"However, when Sauron put the Ruling Ring on his finger, the Elves were immediately aware of him and took off their Rings."
The Dwarves did not remove the seven rings they received but were the most physically and mentally resistant to Sauron's corruption and attempt to bend them to his will. Instead they were driven to extreme greed and a hate for anything prevented them from attaining wealth.
"Whereas the Men who owned the nine Rings were corrupted and became the Nazgûl, the Dwarves were unaffected, save by an increase of their goldlust and hatred for anything that stood between them and what they perceived as their treasure."
And, of course we know what happened to the nine men that were given rings. Who above all else, desired power.
As mentioned earlier, the One Ring had different attributes than the ones that were slaved to it. The One Ring had certain amount of self awareness and self control, as it could change it's size to fall off of the person wearing it, as it did with Isildur and Gollum or use it's own innate power to compel the wearer to a degree in order to benefit it's return to Sauron.
"While separated from Sauron, the Ring would strive to return to him, both by impelling its bearer to yield to Sauron or his servants, or by abandoning its possessor at key moments"
The largest factors in why Gollum "freaked out" over the ring seems to be his own inner nature as well as the means by which the wearer obtains it. That would mean that Smeagol already had greed, jealously and the willingness to commit murder in his character, the Ring simply amplified it greatly, and his act of killing his cousin Deagol to get it, increased the effect of corruption even more, whereas Bilbo simply found it and was not willing to kill even someone like Gollum in the process of escaping.
It's worth noting that even though Deagol only possessed the Ring for a brief few minutes, it seemed to have already been affecting him before he actually found it, thus leading him to refuse to give it to Smeagol as a birthday gift which led to his death and Smeagol's banishment, which allowed the Ring to corrupt him almost entirely over the course of centuries without interference.
I hoped this was a viable answer for you. If you would like to do some more digging in to the matter I will post the link to the LOTR wiki where I found my information. Enjoy and watch out for farmer Maggot!