The benefit of moving to one of the no income tax states is pretty apparent. You do not need to pay income taxes on your income, which means you can keep more of your money and use the savings to invest the money. With more money, you can seek out more investments for your Roth IRA or other retirement accounts.
The perception is that the less income tax you pay, the more you can save. That is true in that assumption. At this point, you need to look into what states will do to generate income.
You need to ask if having no income taxes helps the state to do better than other states. Looking at the research, four of the top ten states with the most substantial economic projections are those states that do not have an income tax. That can be for a variety of different reasons.
Living in a no income tax state is all about your finances. There are a couple of factors that can affect your decisions. It would help if you thought it was worth it, so you save money on your income. Do realize that these states impose other types of taxes as well to raise money.