Well... I think that Claire and Adam have the same power.
Claire can regenerate. Adam can regenerate. Both had their powers 'activated' around the time of the eclipse. We know that the Company knew Claire would be special when she was born, probably due to the fact that they knew the mutation was genetic and both of her parents were special (although both sets of powers might not have manifested yet. I will go into that further below). That said, this is where it gets kind of messy in terms of the activation of powers.
Ok so we know the old crew all had their powers activated when they were younger, hence the formation of the Company and other things. Here's where I get confused. Meredith controlled the fire that 'killed' her and Claire so that it would appear like they died. (I don't believe for a fact that she thought Claire was dead. I just think she didn't want anything to do with her/wanted her to have a better life than she could provide, so she pretended Claire was dead.) Kaito alludes to the fact that Claire's powers had not manifested yet but they knew she was different when he gave her to HRG for 'safekeeping'. In the episode "6 Months Ago", Nathan's powers manifested and he accidentally flew out of his car, which caused Heidi to become paralyzed. HOWEVER... he and Meredith are around the same age. Is it really the eclipse that activates their powers or is it something else? Shouldn't Nathan's flying ability have manifested at the same time as Meredith's?
Ok that tangent aside, here's where I'm going with this. If it IS indeed the eclipse that enables one's powers, Nathan's should have manifested at the same time as Meredith's. We assume the eclipse in 1671 activated Kensei's regeneration, much like the one in May of 07 (thereabouts) activated Claire's SCR and most of our heroes' abilities.
But what if the eclipse is just a coincidence (unlikely but possible)? Who's to say that Kensei's powers had already been enabled by the time Hiro found him? It seems to be that he really wasn't putting himself in the line of fire, what with having decoys pretend to be him, drinking and basically doing nothing whatsoever. He could have already had his power but nothing happened to prove it to him until Hiro showed up.
And maybe one's progression with their ability is not learned, it's acquired. Perhaps Kensei had had his powers for some time, but having fully matured into a man, his regenerative abilities just started repairing the cellular decay that comes with aging. Our bodies are meant to fight diseases and infections... perhaps the part of his brain that controls his power sees the decaying effect of time as an infection and destroys it like white blood cells create antibodies to keep us healthy.
The same thing could happen to Claire once she is fully matured. I'm not saying I'm completely right, but at least it's a possibility. It makes more sense to try to reason it out as to how they could have the same powers than to try to find way to disprove it

I hope that makes sense. I've not had my coffee yet.