Well, Movie!Cap used guns too, as necessary, and my guess would be machine guns on Eldritch Monsters or something instead of actual people.

But as for the crankiness, yeah, that's probably angst with a side order of insecurity - Steve sort of fell into leading (not into being a soldier, but into being a leader) during the war, so he's probably unsure of how to deal with a challenge for power in a group of strangers he's supposed to be leading in a highly charged and unfamiliar situation.

And of course, put Tony in an unfamiliar situation and he will start mouthing off, so... I can see how it would take a bit to straighten everything out.