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.