Well the kinetic energy only comes into effect if you vary your speed, which in real life happens, it's impossible to maintain a perfectly constant speed, but as this is a theoretical discussion I think it's safe to disregard this. Arguments could be made both ways as to whether this effect is greater climbing due to greater fluctuations in speed, or on the flats due to the velocity being higher.

On a different note, though possibly not the most applicable I think discussions of this nature are generally interesting, and it seems to be quite a civil discussion at that.

For those who have some time:
So the way that has been mentioned to look at this is a person with a given “cross sectional” area (more like frontal area), producing a given power, with a given amount of mass, will have two speeds corresponding to flat land and different inclines (dependent on hundreds of other things, from the density of the air to the type of clothing they’re wearing, but I think this is a reasonable rough assumption). So a proportionally high frontal area to mass, produces a good climber and likewise a proportionally low frontal area to mass produces a good flat land rider. Frontal area is roughly second order and mass is roughly third order proportional to radius (of course people aren’t spherical, but…). So people with large radius are better at flats and people with small radius are better at going up hills, look we have a hypothesis that accurately predicts observed data (yay for us).

The possibly more interesting question is, is power constant from flat lands to climbing? I’d think that climbing uses a somewhat different position and also usually involves working at a different cadence, so someone could be relatively better at climbing or flats relative to their “radius” depending on how they react to the changes in these factors? That’s something to chew on isn’t it?