For me, it also depends on the temperature and duration of the run. Running in pouring rain when it's 60s F or warmer can be fine, because it's just helping you cool off. For me, there's a boundary in the 50s to 40sF where the pouring rain makes you get soaked and way too cold. At that point, I would rather the falling rain be falling snow.
The duration of the run also folds into that. Running in pouring rain for less than an hour is totally different than say 2+ hours. For one thing, longer duration runs mean a lot more chafing if you are soaked through. I once did a half marathon (2:12-ish) in about 50 deg F and pouring rain the whole time, and I swear I was chafed over half my body despite the BodyGlide.
Also, for me, running in the rain requires a baseball cap to keep the rain from falling directly into my eyes.