CO division in IDPA is based on ESP division. Basically take a ESP gun and put a dot on the slide. Advantages here over USPSA are that you are allowed a magwell and single action only firearms. Disadvantages here are every pistol in IDPA is limited to 10 rounds in the mags, and the weight limit is challenging to meet with some guns.
CO in USPSA is based on Production division. Must be a gun from the production approved list, with a dot on the slide. Production is 10 rounds only, while CO is whatever you can fit in a 140mm magazine. (23+/-) A recent change in USPSA Production and CO is the 59oz weight limit for any make/model. Aftermarket slides are allowed now as well. Advantage here over IDPA is the round capacity, weight limit, less restrictive holster placement rules, and well none of the weird IDPA rule stuff. Disadvantages here are you can't use a SAO gun, and you can't have a magwell.
ETA: shoot either the shadow 2 or the x5 in USPSA CO with extended mags.