Dreamworks should definitely handle Legend of Zelda, not Illumination

I don't know how much overlap there is, but based on the newest Puss in Boots and their track record with similar IPs like Kung Fu Panda and How to Train your Dragon, I think they're the studio for this.

The mass appeal is a lot more limited, though, and comedy would pretty out of place in a Legend of Zelda film. They would need to push it more towards teenage/adults perhaps like Shrek but with way less comedy elements.