^ Its known everywhere that Dubai is expensive, but to tell you the truth it has everything you need from very cheap to extremely expensive products. So it really depends on where you go to shop.
Its funny how everyone comes to Dubai for shopping, whereas the people of Dubai travel abroad to shop =P
Since I am from Dubai and live here permanently here are a few places for shopping:
Mall of The Emirates (Harvey Nichols)
The Village
Wafi Center
Burjuman Center (Saks Fifth Avenue)
Emirates Towers (Villa Moda)
Mercato
For low-priced materials, accessories, etc. you must check out Mina Bazaar & The Global Village
taz Dubai Mall is not yet opened, the tower itself is still under construction.
Talking about prices, high-end designer stores are usually priced the same as everywhere else. Today, Gucci and some other stores started their sale, but usually most products are gone the first day of sale so I don't think you'll find anything worth buying (on sale) by the time you come.