TAG and Rado are timepiece specialists that started as watchmaking companies, while Gucci is a fashion brand that eventually acquired its watch licensee (Severin Montres). Gucci has the most fashionable and detailed timepieces of the three, and many of their styles are very distinct.
TAG is owned by LVMH and has a lot of basic styles, along with sportier chronographs and the like. Of the three you listed, they have the most "safe" and varied selection.
Rado is held by Swatch Group, and specializes in futuristic, minimalist, and scratch-resistant materials. They have a LOT of dark metal/material watches (black bracelets, black dials).
Of the three, TAG is probably the most prestigious...at least in regarding points of sale (they are very picky about retailers, and they like to have a LOT of case space), but it is also the most common/widespread.