I had both (still have the Lynx), and overall I'd say they were comparable, but I'd put the GG slightly ahead for the better game library, the slightly better screen, and slightly smaller dimensions. The Lynx had slightly better hardware, but in practice I don't think it made a huge difference to the games they were able to make.
Don't think I forgot about the good old Lynx though! Many hours of my youth were spent playing Toki, Kung Food, Rygar and Batman, and others.