Dubai is no longer a discount shopping paradise. The malls sell goods at prices much the same as you will find in any large international city. Electronics are maybe 10-15% cheaper, but clothes are more expensive. You can find excellent knock-offs but it is risky to buy these as they are illegal and can be confiscated. The famous duty free at Dubai airport is hugely disappointing - I found prices to be at a premium here and nothing constituted a bargain when compared with London or New York retail prices.
The other aspect to shopping in Dubai is that at least in the malls, the staff are completely useless - they know very little about the merchandise and are quite unfriendly too.