The problem with the internet is it is so easy to spread mis-information because people say "I read this somewhere" and don't bother to think of WHERE they read it...when that place is usually some crappy blog.
I have done research on lotteries, and while I didn't do ALL states, I never came across ANY that stopped annual payments upon death. They all (and definitely including Mega Millions and Powerball) continue to pay out to your estate upon death. Even most "Win for Life" payouts have a minimum payout so if the winner dies of shock right after redeeming the winning ticket the estate gets something. For example, NY's $1000 a week for life pays out at least $1 million over 20 years.
As for which would you take, well..OBVIOUSLY you would take the lump sum with the interest rates at historic lows. The way they pay out lottery winnings is they invest some amount that would cover the annuity payments. So..if you won a jackpot of $250 million, they would invest whatever it would take to pay you $10 million a year for the next 25 years. That amount iss what they pay out as the lump sum for those who take the lump sum. (Which these days is something like 90% of players.) The lower the interest rate at the time of the investment, the more they have to invest, and therefore the higher the lump lump.
Since we are at historically low interest rates, the lump sum percentage is the highest it has ever been, and likely will ever be again. Chances are, interest rates will rise over the next 25 years and will average considerably higher than they are now. So even simple, low risk investments would likely result in a higher expected value for people taking the lump sum.
I started doing this research about 12 years ago when interest rates were extremely high. At that time, the lump sum value was something like 45-50% of the advertised jackpot. Before taxes. Compared to today where it is around 70%. (This will vary from game to game as some games have 25 equal payments, while others have 30 years, and still others like NY state have a ridiculous 30 or more year payout, with a backended payout system. This greatly decreases the lump sum amount.) But even then, with a halfway decent investment portfolio, you are almost certain to get a better return on the investment of the lump sum than the government would.