The Germans after the battle were done. 100,000 Germans were killed and their warmaking capacity severely hampered. Yes it was an American victory and anyone that says otherwise is ignorant of military history.
Two of my uncles participated in the D-Day invasion. One with the 82nd Airborne, the other with the 101st Airborne.
The uncle with the 101st was also in the Battle of the Bulge and was wounded. He passes away a few year ago and I was a pallbearer at his funeral. He was buried with full military honors. I went up to one of the young honor guard members standing in the funeral home and told him a little history of the man laying in the casket. His eyes got as big as saucers and as I told him about the 17 year old country boy from NC that went through pure hell for his country. My uncle Willie kept his military momentos in a little wooden box and every time I would go and see him I would always ask to see them. He was so proud to be a veteran of WW2, but the more he talked the more his eyes would swell up, because he would always talk about his buddies that had died and he felt guilty for the rest of his life for not dying with them. He was 86 years old when he passed and one of the finest men I have ever known in my life.