Ok, fair assessment of your read, appreciated. Here's what I see from flat/fair more or less, depending on the proponent. Everyone would pay the same percentage, some making a deviation below a certain point. Some make some deductions, other no. I believe it's the fair tax that includes a sales tax.
In any case, to my way of thinking both are regressive, as all of my purchases are necessities. When it comes to sales tax in the great state of Illinois, the state, city, county and sometimes township get in on it. I live in DuPage, which has a substantially lower tax than Cook, (Chicago).
Most of my neighbors have much higher incomes, 3-10 times my income. That the roast we buy might have all bought for Christmas dinner is taxed exactly the same, is by my definition, (the normal definition), regressive.
I'll stop here, see what others have to say.