"one tax law as it would under another tax law" = "under two different tax schemes"
I see you like to play word games.
A sales tax and a flat income tax (at the same rate with the same deductions) are "economically equivalent".
Only problem is no-one is proposing a flat income tax with the same taxbase as a retail sales tax replacing both income and payroll taxes.
No if you want to compare apples with apples and real proposals out there, I am interested in doing so. However, what I am not interested in is perpetuating the income tax in any form, whether it be flat or otherwise. We have already been there and done than and a century of experience tells us what a flat income tax becomes.
"A hand from Washington will be stretched out and placed upon every man's business; the eye of the federal inspector will be in every man's counting house....The law will of necessity have inquisical features, it will provide penalties, it will create complicated machinery. Under it men will be hauled into courts distant from their homes. Heavy fines imposed by distant and unfamiliar tribunals will constantly menace the tax payer. An army of federal inspectors, spies, and detectives will descend upon the state."
-- Virginian House Speaker Richard E. Byrd, 1910, predicting the consequences of an income tax.
There is also plenty of evidence from every single continent on what a sales tax becomes when its rate gets too high: A VAT!