Income tax is progressive; sales tax is regressive.

That is implementation specific. And oversimplified. An income tax is regressive if you only look within a tax bracket including the highest one which arguably contains the highest level of disparity within it (quantitatively, though perhaps not qualitatively). More so income tax on capital gains. Just the ability to have the majority of your income taxed as gains is regressive. Sales tax that are limited to luxury goods are progressive. Food assistance is often exempted from certain sales tax, which is progressive.

We can make either type of tax regressive, progressive, or vary by income level to push people toward the median lifestyle.

Implementation costs and the ease of avoidance should be larger concerns I think.

In Nevada there's no income tax, some sales tax, but the vast majority of taxable purchases are luxury purchases made by wealthy tourists and there's also a hotel room tax.

So in that one case, choosing sales tax isn't regressive.

I know and generally I agree with taxing income for this reason. “Double taxation” is a silly reason.

Agreed. Especially given the wide range of sales and income tax rates.

The double taxation criticism was about sales tax.

I know. Not only is it silly to call it a double tax, it’s also not even correct. Even in NH that money is taxed at least 3 other times before you spend it. Sales tax would be at least the 4th tax on the same money.