I ride because I love it, run because I have to. I would rather ride up the steepest mountain pass on my road bike or the rockiest climb on my mtn bike than run up a nice, well paved slope. Run, for sure.
Having said that, while I can pretty much spin up any hill on my road bike (with an exception once when I shot out of an alley onto the middle of a really steep hill, totally unprepared and geared way too high...I pulled it off and didn't fall, but it was UGLY) there comes a time on my mountain bike where I just have lost my momentum and hit a rock and topple over. I usually can unclip, grab something, or tuck and roll.
If I ran up the same hill, I would have to stop and do CPR on myself.