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I think that Spock's "later years" happened after Kirk's since Spock was in several NextGen episodes.. so it's feasable that they could be around the same age.
Spock is much younger than Kirk, as he died stabilizing the warp drive in Wrath of Khan, then was launched to the Genesis planet, where he was reborn, and aged at a great rate until his removal from that planet, at which time he was taken back to Vulcan to get his edumacatiom.