GIMP and Illustrator are very different. GIMP is similar to Photoshop, it's made to edit/create pictures (and logos). Illustrator is a vector drawing tool, that is mainly done for creating stuff from scratch. I'd recommend Illustrator for logos, because it creates better looking logos, and you can easily modify a logo when you want to change something. Also, Illustrator lets you scale your logo without loss of image quality, because it uses vectors. Hope this helped!