This *really* isn’t something I know enough for confident proclamations, but I can toss out some factors:

- Prussia was doing a lot of the heavy lifting of suppressing the revolutions of 1848, and could see what would eventually be the Austro-Prussian war looming on the horizon

- The German Confederation wasn’t very good at marshaling forces under unitary command, not least because there was competition for leadership between Prussia and Austria

- Denmark in contrast coopted its liberal revolution pretty smoothly and entered the fight unified and undistracted

- the Prussian leadership didn’t particularly want the war - German nationalists gave it to them as a fait accompli. With the ultimate goal of building a Prussian-led Germany, they needed to do something to retain public confidence as a vehicle for German national aspirations, but upsetting the balance of power risked drawing major powers into an alliance against them. It’s not obvious that they wanted to win, or that they’d be better off if they had.