A calcium reactor works by dissolving what are essentially dead coral skeletons and putting the effluent back into the tank. As a result, it provides provides both Ca, Alk and Mg as well as trace elements.
Here's a Randy Holmes Farley article comparing various methods of Ca/Alk supplementation:
http://209.85.173.132/search?q=cache...lnk&cd=3&gl=ca
Here's one of RC's interminable threads with people arguing back and forth about the merits each method. As usual, it was finally closed due to it degenerating into personal attacks:
http://www.reefcentral.com/forums/sh...5&pagenumber=7
Randy also has another article which I can't find now comparing the relative costs. The conclusion I believe was that the bigger the tank you have, the more cost efficient a calcium reactor is in the long run. The "tipping point" where a reactor becomes the better deal was around the 125 gallon mark, I think. The costs he calculated were with respect to his two-part method using bulk CaCl, baking soda and MgCl/MgSO4 rather than fancy German dosing pumps with pretty labelled CaCl, baking soda and MgCl/MgSO4 which cost more.