Re the Vietnam-U.S. question, maybe a little analogy would clarify.
I step into the ring with Mike Tyson. In the course of one round, while the crowd boos, I manage to hit Tyson once and split his eyebrow. He splits both my eyebrows, blacks both my eyes, breaks three of my ribs and sends me down for the count twice. At the end of one round, concerned with the booing and the state of Tyson’s eyebrow, and having already earned the meager purse, Tyson’s manager throws in the towel.
Now, I have won the fight. Nobody disputes that. But it would be questionable, to say the least, to thereby conclude that I am a better boxer than Mike Tyson.
Likewise, nobody disputes that the North Vietnamese won the Vietnam war. We gave up before they did, so they won. But it’s a non sequitur to conclude from that that North Vietnam fielded a qualitatively superior military force.
Re the OP, I would suggest the German Wehrmacht of World War II was the toughest we faced. It’s true that the British whipped us pretty thoroughly in 1812, but I humbly submit that was more because we were so bad than because the British were so good. Against a nastier opponent like France, the British lost quite a number of battles, even with allies to help them. Even we Americans could beat them when properly trained and led, as at New Orleans. But the Wehrmacht gave everybody a very hard time, and it took us, the British and the Russians together to bring them down.
I would definitely not nominate the World War I German military for anywhere near the toughest we faced. The fact is, the Germans in that war were just about as inept as the Allies; we just hear less about it. The mixup about which side of Paris to march on, von Moltke’s panic, the Verdun offensive, and the stupidity of not even having a plan to go to war against Russia alone were all unforgivable military blunders, IMO.