Norway has one of the highest gun ownership rates, and until some years back the territorial army had people keep their AG3 service weapons at home. Yet it's only been for time limited periods that police has been routinely armed, and they certainly also doesn't act like the US. I don't like guns, but I also don't think guns alone are sufficient to explain the high firearms related crime rate in the US.
Some of the differences:
1. a different gun culture. Most weapons in Norway are actually for hunting, and no that does not mean semi-automatics etc.. A few are for firing on a range, but there's no culture for seeing a firearm as intended for self defense, and the laws specifically makes it hard (you need to store the weapon locked down and inoperable, and generally you'd e.g. store gun and ammo separately; if you have time to arm yourself, police will question whether or not you had the ability to get away and call for help instead - if the threat is not immediate enough you risk a murder charge).
2. A culture for not meeting suspects with force unless they're armed, and generally focus on de-escalation, and for taking weapons use extremely seriously. E.g. officers need to account for every time they take their weapon out and every bullet fired.
3. A legal system that is generally lenient but where there is a clear path of escalation in response based on how dangerous a crime is. E.g. a robbery carries a sentence up to 5 years if unarmed, of which you'd generally serve less than half (and most people won't get the maximum sentence) - as an example, a robber that participated in a stealing one of the instances of Scream and Madonna by Munch got 2 years and 6 months a decade and a bit back.
Arm yourself, and you risk an additional 7 years. Kill or seriously injure someone during a robbery, and you might get 21. As an example, one of the largest armed robberies in recent Norwegian history, that ended up with one dead poice officer, (the "Nokas" robbery) ended up with one of them getting 18 years, and several others getting 16. That's a pretty substantial extra risk on top of the risks involved in a shootout with police.
Combine that with #2, and criminals have a very strong incentive in general for not being armed - by not arming themselves they don't risk being shot at by police, and they cut the worst case punishment from 21 to at most 5 years in a robbery, for example.
Compare to the US, where a robber has little reason to want to take the risk that police won't shoot even if they're unarmed, given how often we hear of police firing even at innocent civilians. Couple that with high sentences and the incremental cost in using firearms to prevent police from catching or killing them is low.