I've been running for years and only my left IT band has been sore lately. No recent injuries (rolled my last ankle something good 7 months ago) and haven't added any additional mileage lately. I would expect both legs to tire evenly. Is it uncommon to experience this from running?
I know that my most frequent running injury was my right hip. Never had a problem with my left side at all.
I think you usually end up injuring one side early in life, then compensate or lose flexibility somehow, then start developing imbalances. I'm a huge barbell fan, but bodyweight single-left stuff is awesome for identifying imbalances.
I would imagine every human being that masters the pistol squat had to spend a lot of time dealing with the differences between both legs. I was able to knock out ~10 on my right side and could barely do ~3 on my other, before I started really going after the imbalances.