A calcium reactor uses carbon dioxide to dissolve the calcium product. You need to refill your carbon dioxide tank periodically, in addition to replenishing the media. Usually the equipment cost of a calcium reactor is substantially more than a kalk/nielson reactor, because you need to buy the reactor, the co2 tank, a regulator, bubble counter, and maybe more (not sure here).
A kalk/nielson reactor only needs to have kalk added to it periodically. It is essentially a reactor tube with a mixing device, either a power head or a stir bar. The powder sits on the bottom and the kalk saturated water is drained off the top and into your tank/sump.
I'd estimate that a calcium reactor will run you $350-450, while a kalk reactor is $200.
I'm not sure I agree that the cost of media for the kalk reactor will end up making that system cost more over time. The $150 minimum price difference can buy a lot of kalk.
From what I read here, the real difference is that a calcium reactor is generally capable of adding more calcium to your tank. So if you have a tank that is a calcium hog, the kalk reactor may not be able to keep up. Having said that, some people run both, and it seems like many people get a kalk reactor first, and then if/when their tank starts needing more calcium, they get a calcium reactor. This certainly seems to be the more prudent economic way to do it.