Well, to be honest the only thing they really have in common is the fact that they are both opiates. Codeine is a pro-drug for morphine which must be metabolized by the liver to become active. Oxycodone on the other hand is not a pro-drug, and much more powerful than codeine.
As far as subjective 'buzz' effects go, oxycodone is usually regarded as more stimulating and has more euphoria IMO. Although there is nothing wrong with codeine, oxycodone is obviously preferred by most.
I'm not really sure what else there is to say, really. It's like comparing apples to shittier apples...I guess.