http://en.wikipedia.org/wiki/Simplified_Spelling_Board
The SSB, an American organization in the early years of the 20th century, sought to consolidate English spelling for the purposes of clarity in international communication. The organization was far more effective in furthering their views in the United States than abroad, and their proposed simplifications were to use ‘Z’ when the “zee” sound appears so as to distinguish it from the “s” sound. Phonetically, the two sounds are identical, but one involves the use of the vocal chords (‘Z’), while the other does not.
Generally, I find the Z spelling more correct; the more differentiation between word spellings, the better, and the closer a spoken English word is to its spelling, the better. They are also responsible for the more-intuitive “theater” (compared to theatre) and color (colour). These words, and the general class of words they belong to, are counterintuitive in British English.
Objectively, though, one shouldn’t become too obsessed with minor spelling differences like that. Standardized spelling is a fairly new practice in the history of language, and there’s a lot of reason to believe that standardized spelling has actually reduced the expressive capability of the languages that use it. We would generally consider “aks” as an incorrect form of “ask” (“Let me aks you a question”), but middle English sources use both forms and sometimes in different contexts. Further, there are stylistic rules that nobody here would know about, that only a well-schooled copy editor would ever pick up. If you’re writing a web site for copy editors, you should know the rules so as to not look stupid, but most normal, sane people aren’t going to care or even notice. So, I guess the point I’m trying to hit is, it doesn’t matter. Do whatever.