Oxygen absorbing cap have an extra coating that literally absorbs the oxygen from the headspace of each bottle. In theory, this promotes better, fresher beer. However, most peeps that use them don't notice that much of a difference. The ratio of oxygen to beer makes absorbing that 1 oz or so of oxygen pretty negligable, so it would be expected that it doesn't make that much of a difference. CO2 is also denser than O2, so as soon as your beer starts carbonating, there is a layer of CO2 betweent he beer and the O2 anyway, so no real effect on the beer anyway.
The regular crown caps are what most everyone uses, and they are fine and obviously cheaper than the O2 absorbing caps. You are good to go with those as well.
Primary #1 - Midnight Ryeder (Midnight Wheat and Rye)
Primary #2 - Florida Weiss
Primary #3 - Kane-DOH APA (Honey Citra APA)
Secondary #1 - Downtown Flanders Brown (brewed August 2012)
Keg #1 - Raspberry Florida Weiss
Keg #2 - Cinnamon Raisin Cider
Keg #3 - NONE!
Bottled - NONE!