The weaponry.

Guns. The bread and butter of the armies.
For a long time there was no real change in muzzle loader guns. There were experiments, Prussians tinkered with various configurations (changing the shape of stock, stuff like that), but nothing revolutionary came from it. Then in the first half of the 19th century a new firing mechanism was introduced, the percussion cap, and the Austrian army also started to phase out the old flintlock system (which was introduced in the 1500s!), and 1842M Augustine infantry musket entered into service. This war of independence was the field test of the new guns.
Basically instead of the spark of the flint, a chemical reaction induced the ignition of the gunpowder which was stuffed down the barrel. See the animations.
The freshly organized Hungarian army's greatest challenge was the procurement of guns. They had what the regular units had with themselves, the new percussion cap ones, they had warehouses with the old flintlock system, but there was little to no manufacturing capacity, which needed to be set up. They also tried to alleviate the hunger with foreign purchases and requisition of civilian hunting arms, mostly flintlock muzzleloaders - often recruits simply brought their rifles from home with themselves. In the active phase of the war, after won battles and sieges, they also make good use of the captured equipment. They needed all guns, pistols, and carbines what they could get, from any source available.
The 1842M had a rifled version, sometimes called 1844M, used in way smaller numbers, mostly in border guard units, jäger, sharpshooters. While I "researched" I found a note that in general all over Europe, rifled guns were frowned upon, and their users were considered murderers. Early rifles were hard to use as the bullet was hard to press down the barrel, due to tight fit, but this 1844M was almost as easy to load as the smoothbore muskets.
Flintlock guns came at least in four variation, 1798M, 1807M, 1818M, 1838M. Imported weapons came from England and Belgium, percussion primer, some rifled.
Apparently a gunsmith in Kassa invented a breach loading system and offered the government his work. It could have been a paradigm shifting event, unfortunately the country was in no position to invest in a new and untried piece of equipment, especially not in a number that could make the difference.