AFAIK, the hour record for cycling ascent is by Pantani on a Giro climb, about 6000'/hour. The record for running a vertical kilometer is 28'. so that's pretty close. I don't know of a record for cycling a vertical k.
I've ridden with a runner on a long climbing ride. He did great, beat me and hung with the fastest members of our group. He climbed much better OOS than seated which is not the norm for cyclists. He was a fairly light guy, like most runners, probably the best BMI of any of us.
On any normal cycling climb, a person on a bike will outclimb a person on foot who is not carrying a pack, not even close. It is NOT faster to get off and walk the bike up the hill. A 4' mile on the flat is of course 15mph. TdF pros average 13.8 on climbs and for considerably longer than a mile..
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