The First Danish-Prussian War ended in the opinion of the population, army and politicians with an overwhelming Danish victory.
It came in handy after the many disappointments during the previous 50 years. The loss of the navy to England 1807, the state bankruptcy in 1813 after the Napoleonic Wars and the loss of Norway in 1815.
A romantic national movement got a huge boost, and the worship of the flag, king and country took new heights.

But the victory was on a cheap basis.
The defeated were rebels without much military prowess or large funds in the back. As soon as the German Confederation came to the aid, it hit the Danes hard.First after the Prussian General Wrangel and his confedered army, after international pressure, moved away from Fredericia and back across the border to the south that the Danes gained momentum.
If Wrangel and his troops had been present at Fredericia, the counterattack in 1849 probably would have ended with a Danish massacre.

And the “victory” solved nothing. Tensions between Holsten and Denmark in particular, continued, and 14 years later a new conflict arose on the same theme.
And this time it ended with Danish defeat and a deep national depression.