I live in a no tax state (though it isn't why we moved here and I don't like living here in most ways). I think it mostly matters when moving from a state with very high overall tax burdens (eg New Jersey, Oregon, etc) to a state with a lower overall tax burden (even if there is a state income tax). We save, I think, a few thousand per year over most other states. We save more as our income goes up, and as we keep our house and discretionary spending stable, and of course we save a lot compared with if we were living in New Jersey, Oregon, etc.
But low taxes = fewer amenities and fewer social services. I grew up in a medium high tax state that had far nicer roads, parks, social services, public spaces, etc, than the state I live now.
And no income tax means lots of sales tax and property tax. We pay ~6K/year property tax for real estate worth 200K, and it's been going up notably almost every year.