Ryan survives, Miller does not. Humaneness is not rewarded in war, but Miller doesn't want to die knowing it's all in vain. Just before he dies, he tells Ryan to be worth all this. There is a glaring contrast between the actual film, and its prologue and epilogue. The first images show a present-day family visiting a war cemetery.
Grandpa leads the way and stops at one of the numerous white crosses.
This sequence is adorned with a flying American flag, and it's rather depressing. He lives in the suburbs, does his job, loves his family, watches television, and knows himself save in the fatherland. Your heart misses a beat, but once you're on the Normandy beach, the prologue is forgotten. Grandpa appears to be Ryan, and the grave he stands at is Captain Miller's. Ryan is overcome by his emotions, and his wife comes to his aid.