Sure, President Snow is dead along with his likely successor Coin who was likely no better. But did things actually improve for people at the end? Sure, no more Hunger Games but did poverty and hunger improve? I don't think that was clear in the end.
Apparently, yes it did.
Canonically, all the information we have on what happens after the war comes from the end of the last book Mockingjay. So we don't have a full picture, but we can work out a few things.
The incorrigibly upbeat yet endlessly cynical Plutarch Heavensbee gives a mixed assessment of the future:
The truth is, no one quite knows what to do with me now that the war's over, although if another one should spring up, Plutarch's sure they could find a role for me. Then Plutarch has a good laugh. It never seems to bother him when no one else appreciates his jokes.
"Are you preparing for another war, Plutarch?" I ask.
"Oh, not now. Now we're in that sweet period where everyone agrees that our recent horrors should never be repeated," he says. "But collective thinking is usually short-lived. We're fickle, stupid beings with poor memories and a great gift for self-destruction. Although who knows? Maybe this will be it, Katniss."
"What?" I ask.
"The time it sticks. Maybe we are witnessing the evolution of the human race. Think about that."
-- Mockingjay, chapter 27 (emphasis mine)
But certainly on the timescale of a year and even ten years, life seems to have improved enormously, at least in District 12. People work together, using Capitol technology as well as their own strength, to make it a decent place to live. They're not slaving their lives away in the mines any more, but preparing to build a medicine factory:
We're not alone. A few hundred others return because, whatever has happened, this is our home. With the mines closed, they plow the ashes into the earth and plant food. Machines from the Capitol break ground for a new factory where we will make medicines. Although no one seeds it, the Meadow turns green again.
-- Mockingjay, chapter 27
And by the time of the epilogue, not only are the Hunger Games a distant memory, but the old way of life is so far removed from the new era that Katniss fears her children will be "frightened to death" even to hear about it:
The questions are just beginning. The arenas have been completely destroyed, the memorials built, there are no more Hunger Games. But they teach about them at school, and the girl knows we played a role in them. The boy will know in a few years. How can I tell them about that world without frightening them to death?
-- Mockingjay, epilogue (emphasis mine)
So the new Panem is clearly a much happier and more prosperous place to live than the old Districts, while presumably being less comfortable and cloistered than the old Capitol.
However, as pointed out in comments, the continent is still recovering from the apocalyptic events that turned North America into the tiny and stunted (population-wise) Panem. It's never made entirely clear what these events are, but recovery from them is going to take longer than a few decades. But people seem to be (finally) pulling together in trying to improve their lives, using the resources of the Capitol for the needs of the many rather than the pleasure of the few.
TL;DR: life isn't perfect, and never will be, but YES, the living standards in the Districts and the social organisation of Panem are now much better than they were.