It's all relative. Compared to a place like modern day Chicago or Baltimore, even if you account for the fact that you are looking at drastically different sample sizes, the relative percentage of violent crime is actually a bit worse today, but only if you look at verified records. In other words, as historians, what we can prove based on reliable crime statistics (culled from newspapers, police reports, etc.) don't show the "Old West" to be any more violent than your normal American metropolis in the 21st century.

In this way, you could say that things like the Gunfight at the O.K. Corral are indeed the rarity and not the norm. Now, that said, you could probably make the case that the "Old West" was indeed a more dangerous place than your modern American metropolis, in that people died of disease with greater frequency and at younger ages than what we see today. There was also a greater incidence of accidental deaths via (and this happened quite a bit) horse-related accidents, not to mention work-place mishaps. People got drunk and fell off their horses, stumbled under carriages, and just generally hurt themselves to a point where they eventually died a lot more frequently than what we see today. They also died "on the job" with a lot more regularity. This is the result of huge leaps in medicine and workplace safety protocols (and unionization).

TD;LR - The "Old West" wasn't so much more violent as it was just more dangerous in general.

[Sources - Michael Denning, 'Mechanic Accents'; Richard Slotkin, 'Gunfighter Nation']