The difference can be explained by this completely made up example: A steel mill buys iron ore for $1 a kilo and makes steel of that. A nail factory buys steel for $1.50 a kilo and makes nails of that. A distributor buys those nails wholesale for $2 a kilo. A hardware store buys those nails from the wholesaler for $2.50 a kilo. A contractor buys those nails from the hardware store for $3 a kilo. The subcontractor bills $3.50 a kilo for those nails. The general contractor bills you $4 a kilo for those nails.
With VAT you/the general contractor/all businesses involved pay taxes on a total of $4.
With a transaction tax, it would be paid on $17.50.
But the above is a simplified example. In the real world there are probably a lot more businesses (each specializing in their own niche) and therefor transaction involved in getting that nail into your wall.
If you have a product that goes from mine to mill to factory to wholesaler to retailer to consumer, the tax is paid five times. But if the same company owns the mine as operates the retail store, it's paid only once.
That's an insurmountable advantage for vertically integrated companies, so no others remain and tax-wise you end up with the same result as sales tax or VAT (i.e. the tax is paid on the total final value) except that you've needlessly destroyed every non-vertically integrated business.
That is the problem that VAT solves, by giving longer supply chains the same tax treatment as vertically integrated corporations.
http://apttax.com/execsummary.php