This should not be the case. This should, in fact, be the opposite of the case. Playing someone with the mental alacrity of a ball of twine should be much easier than your brilliant wizard. But when you try to play a dumb character, it's easy for that character to wind up slipping into periods of pointless stupidity without acting like any of the nitwits you've actually dealt with over the course of your life.
Intelligence is a hard thing to quantify at the best of times, but some of our characters are meant to be just plain slow. I've played a few, and it's always a challenge to make the character feel like a person instead of a caricature. So here are some tips for making your big dummy feel appropriately oafish and endearing instead of just being a strawman.