Was the war success for the US?

That depends on which aspect you are looking for. They did end WW2 which was a huge success but they did a bear minimum to every other country. In Saving Private Ryan, they made Omaha Beach look so difficult. They actually had the easiest beaches to take, Omaha and Utah, and they still managed to screw up. On their trip there, they got lost and landed far to the south to be anywhere near the beaches that they had to take. The Canadian assault force was stuck with Juno beach. Juno beach housed concrete pillboxes, bunkers and an anti-ship/personnel cannon made soley of concrete and shells. The Canadians had to scale the massive conrete wall while being shot at. They managed to successfully take the beach and capture the town of Caen within 2 days. Which was more successful.