Jim Carey is obnoxious and annoying, and Nicholas Cage is strange and creepy. I don't think either of them is a better actor. I wouldn't hire either of them if I were making a film. To compare the two is like comparing brussel sprouts and spinach! Both are icky and unappealing.
Nicolas Cage is definitely a bigger star than Jim Carrey, whether or not he was in Dumb and Dumber. Carrey is just a character actor, so he plays the same types of roles in every single film. Cage's roles show more versatility, so I believe that he ultimately has more talent.
Jim Carrey and Nicholas Cage are both very successful actors. To say one is a bigger star than the other is just a matter of opinion. They both go through periods between making movies and not. They each have had their fair share of successes and failures. They are both household names.
Just because Nicolas Cage turned down Dumb and Dumber, does not mean that Jim Carrey is a bigger star than him. There's no doubt that Nicolas Cage is a huge movie star, but his choices in roles hasn't always been stellar. He has been up for a number of huge roles that could have been his most famous, if he had taken them.