Yes, there is a difference.
“I feel like the best basketball player on earth” means that you feel like the equal of whoever is the best basketball player on earth. Let's say Stephen Curry.
“I feel like I am the best basketball player on earth" means that you feel that you are the best basketball player on earth.
They're mostly the same, but the former can also mean "I feel the way the best basketball player on Earth feels", which carries with it the implication that said player isn't you.
Yes. The first one means your comparing yourself to the best basketball player while the second one is a statement that you consider yourself the best.
It's a bit like saying I feel like napoleon and I think I'm napoleon
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They both mean the same thing.
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