From a quick look at Wikipedia (not exactly the gold standard of research, but hey) the US has a truly astounding suicide-by-firearm rate compared to the UK (7.1 vs 0.15), but if we only compare homicide-by-firearm it's actually even worse than before (4.86 vs 0.06 -> ~80x higher, but it's unreliable because we're dividing by such a small number). But then our income inequality is at least a bit higher than the UK (41% vs 34% Gini coefficient), we certainly have substantially worse social safety nets across the board, and we have serious systemic socioeconomic issues in a downright embarrassing number of locations.
But to me at least, by far the most important factor is one I can't easily turn up reliable statistics on - gangs, cartels, and other organized crime. Having lived in some questionable areas, I've seen first hand that in many cases criminal groups will engage in conflict with one another and not intentionally target innocent bystanders. I used to live in an area where there were nightly shootings (!!!) that I could hear from my house, but it was a seemingly mutual exchange of gunfire. I have no idea how you're supposed to account for that sort of thing in an analysis, but it seems clear to me that it must be accounted for if you're going to attempt to claim that it's reasonably unbiased.