The Kelvin, regardless of size, also seemed to be an explorer, otherwise why would you need a ship of 800?
Why would the Enterprise need a crew of 430 when it could be run with a skeleton crew and an automation system? For that matter, why did Pike's E have a crew of 200 and change while the same ship had more than twice the complement under Kirk? There are lots of factors that could determine a ship's complement. The mission profile could be one, but there could be other considerations like the level of technology (more people might be needed to do a given task if it were less automated), the efficiency of the life support systems (I often speculated that Pike's E had fewer crew since it couldn't support as many), the duration of the mission (a given amount of non-renewable resources could support a larger crew if the mission were shorter), and so on.