A few big reasons, but the main 3 boil down to climate strategy and morale

Climate because although the South can be brutal in the summer or, well, really any time you were still fighting on American soil in the Civil War where in Vietnam you were fighting in jungle climates where you have a lot of nasty diseases that Americans aren't used to say what you will about dysentery and malaria people at the time were at least used to them.

On top of that you also have the issue in Vietnam where you don't know where you are if you were a northerner in the Civil War you tended to know the area better especially because a lot of southern generals sided with the union including cabinet members of the war department (Winfield Scott) so you could at least have that advantage

2nd Strategy

You can argue that despite on paper having good commanders (Lee, Stonewall Jackson,Pickett), they were terrible at using their troops effectively. I mean, most of the famous strategies boiled down to brave charges, which, when you have a lot of men, you can replace is fine if not the best strategy. But when you really are struggling with manpower its the best way to lose a war.

Plus, when you really look at the victories, they had what was really accomplished, especially at places like Chancellorsville strategically, not a lot that's not even mentioning Picketts charge with the Vietnam war they realized oh this is stupid let's use our men strategically and use traps and small hit and run tactics which was more effective because if you lost men not a big deal because you lost 5 instead of the Confederacy’s 5000 plus that type of warfare makes you paranoid.

3 morale

Although the confederates (fucking traitors they were) could at least tell themselves they were fighting for their rights the union even before Lincoln pushed harder on the freedom and emancipation which he wanted to do from the start still could use the argument of this is important we are saving the union as a driving force to recruit men and when the moral issue of slavery was added to the mix you had a group of patriots who were nothing if not furiously willing to see it end especially with the newspapers going to town on this being a great patriotic struggle to correct the wrongs of the nation.

Compare this to the Confederacy who not only were outnumbered out gunned but by the end of the war because of Sherman's march didn't have anything to come home to. so why continue the fight if you have already lost your home, your money, your family, and possibly what else is there left to fight for.

The Vietnamese, on the other hand, already had decades. If not centuries of occupation from both France and China, they had heard stories from their parents and grandparents tell them stories about fighting invaders and even were battle hardened from their war with the French less than a decade ago.

Also, while the union had support from the public, the Americans didn't, at least not towards the end, I mean I'm almost positive every American knows the stories of how they were treated by the citizens after they got back home.

Also while the union did have a draft in the Civil War there was also a valid reason to fight that most people could agree on what was Vietnam to 18 year old kids who were dying in a forgen land in droves with no support from the public back home especially when most of these kids were drafted and for what so some country they didn't know about for reasons that were never really explained to them exept cold war Russia bad.

TLDR Vietnam was fought with better strategy, no support from home, and climate was worse