This is the question that a nabar working paper is to be answered by Flake, Heathkot, Storeleton, and Violent. Using various types of survey and administrative data, the author reaches the following 8 conclusions:
(i) The federal tax and transfer system is progressive.
(ii) State and local tax and transfer systems are close to average proportional.
(iii) States have sufficient disparity in tax levels and tax progress.
(iv) states that are mostly funded by sales and property taxes have low in retrograde tax system and low average tax rates. States that are mostly funded by income tax have progressive tax systems and high average tax rates.
(v) The regressive states are concentrated in the south and more inter-state attract pure migration, especially of high-or-high migrants.
(vi) State progress has been widely stable between 2005 and 2016.
(vii) The inclusion of corporate income and commercial taxes reduces average state progress but increases federal progress.
(viii) In the form of a transfer, there is a major positive impact on the progress measured, including spending on public goods and services.
Which states have the most progressive tax system? Alaska, Minnesota, DC, California and New Mexico are at the top.
Which states have the most regressive tax system? Illinois, Nevada, New Hampshire, Tennessee and Texas leads.

Progress is clearly depicted by comparing California and Texas. Both states have a progressive income tax. However, income tax creates a larger part of money in California than Texas and California tax code is much more progressive. State transfer in both states is also progressive, but California has a huge transfer as its budget share compared to Texas. In contrast, sales, excise and property tax are retrograde in both states, but Texas depends a lot on these funding mechanisms. Due to the combination of these funding mechanisms, overall Texas has a highly retrograde tax system while California is highly progressive.

A very interesting expansion can be found in the entire paper here.