The only difference between sales tax and VAT is that VAT is applied at each stage of the production/sales chain, but only on the incremental value added at each stage, whereas sales tax is applied only at the very end of the chain on the entire value. The advantage of sales tax is that only the retail seller needs to worry about collecting it, and the advantage of VAT is that you don't need rules to figure out which stage along the chain is supposed to be the "final" one. (Consider small businesses buying product from a place like Costco. They either get double-taxed, or have to get some sort of exemption.)

In terms of the actual money collected, the two are the same. An X% tax rate results in the retail buyer paying X% more.

The basic answer is that the progressive European countries primarily funded through VAT are indeed using a regressive taxation system, but countering it with progressive spending.

The US system is a moderately progressive tax system but less progressive spending (not no progressive spending, but not nearly as much).

The argument is that you "buy off" the wealthy interests (both wealthy individuals and corporations) by using a regressive tax system, so they are happier to let you spend the money progressively, while in the US they are constantly fighting any progressive spending, because any tax cut will benefit them greatly.

VAT is also a regressive. It's comparable to sales tax.