Actually, there were three times that Frodo put the ring on and nothing
terrible happened. The first time he put it on was in Tom Bombadil's house (to
make sure he got the real ring back after Tom put it on his finger and didn't
disappear); the second was when it slipped on his finger in the Prancing Pony
(the only ill effect was his own embarrasment) and the third time was when he
put it back on after leaving Amon Hen when he decided to go to Mordor alone
(remember, Sam sees the boat "sliding down the bank all by itself"). The only
times something dramatic happens is when he puts on the ring around the Black
Riders and on top of Amon Hen. And both experiences were different. I think
rather than proving your point that the ring is very different in The Hobbit,
it shows that the ring is very contextual. It has different effects, not only
depending on the person, but on where the person is and what is going on.
Also, the first and second times Sam puts it on, it makes things "vague" but
greatly enhances his hearing. The "vision" of "Samwise the Strong, Hero of the
Age" is a fantasy that he has while carrying the ring, not while he is wearing
it.
BTW, Frodo saw the eye the first time in Galadriel's mirror when the ring
wasn't on, and didn't see it on Amon Hen when the ring was on (but could feel
it). The only other time he saw the eye was for real while he was climbing Mt.
Doom and the heavy black smoke around Barad-dur cleared for a moment and he saw
a flash of red light of the eye. What was growing in his mind, after he entered
Mordor, was the ring itself, which was a burning wheel. That clearly had to do
with him being in
Mordor.
"...men's hearts are not often as bad as their acts, and very seldom as bad as their words." Tolkien, letter #250.
