The problem with the state tax issue is, you have to move BEFORE you cash in the ticket. And, you need make sure you are not liable for taxes in your previous state once you do move.
The cash option is about 50% (today PowerBall is 50.8% and Mega Million is 52.7%).
Federal tax rate is 37% max (actually bit less as the first $539,900 is taxed at lesser rate), so you get 18.9% of the jackpot. So a $1 billion jackpot, you actually get a check for $327 million.
Annuities for my age are paying about 8% now, so that would be an income of about $26 million per year for the rest of my life. And the good news is, if you do an annuity, part of the money paid to you is your money, and since it was already taxed, it is not taxed again. So you are only paying taxes on a fraction of that $26 mil.