The previous answers are correct in saying that Percocet is a combination of oxycodone and acetaminophen (Tylenol). For long-term use, oxycodone is better than Percocet because taking too much acetaminophen can result in liver damage.
I am, however, concerned because they told you they take oxycodone more frequently than you do. I just want to point out that they are apparently taking the immediate release form of oxycodone, which is taken more frequently. You are taking the continuous release form, which is released slowly over a 12-hour period. Taking the continuous release form more frequently could be very dangerous.
The studies I've seen that look at long-term use of oxycodone have not shown any significant adverse reactions other than the standard possible side effects listed with the medication. One thing you need to be aware of concerning long term use of oxycodone or any other opioid medication, though, is that it does result in a physical dependence on the drug. If you should decide to quit taking it, it is important that you taper off gradually under your doctor's care to avoid serious withdrawal symptoms.