I don't think intelligence is per se something to be admired. Adolph Hitler was a very intelligent strategist, and actually openly praised for that quality by some contemporary statesmen. Sigmund Freud was very intelligent, but he kept smoking after a few surgeries of his cancerous growths in his mouth. Carl Jung, another in that category contemplated suicide for the most of his highly successful life. The list is very long, pointing at the simple truth that intelligence may not be an advantage after all - if not coupled with some other qualities of more dignifying nature.
Now we would have to step out of the boundaries suggested by the above question and maybe say "who is making more sense". It's pointless to "prove" a belief, which is only a deliberate choice to take something as true - with no evidence necessary. There is no burden of a proof on a believer, so they like turning it around and saying how much of science is based on a belief as well - which they call "theory". The old trick of projection - avoiding the answer by projecting the inability of proof on the opponent.
However, the difference is enormous.
It doesn't matter whether "gravity theory" is provable or not, gravity IS - period. On the other hand religionists can only "believe" that God exists. To that effect, one can say that "there is no God" - and nothing happens as a result; but one can't jump from the skyscraper denying the "gravity theory".
Science is dealing with something that doesn't need "proofs" in order to exist. Religionists are dealing with something that doesn't give evidence of existing - so playing with "proofs" is a game of sheer rhetoric. For example: "An absence of evidence is not an evidence of absence". Or: "If we can't prove the existence of God, you can't prove His nonexistence either". It's silly formalistic logic, and whether you are a theist or atheist you might as well avoid such tests of smartness that are not leading anywhere.
However, just for the heck of it, or for an intellectual sport event - you may want to lock horns with a religionist and play that game for a while. As long as you don't imagine how you have a chance to prove them wrong. It's against their religion to be proven wrong - remember?