Is it generally better for your credit score if you pay off old debts or if you file for bankruptcy?

I have a lot of old, unpaid debts. I estimate my debt to be around $14,000. Most of these were credit cards I opened when I was 18. I was irresponsible with them and I maxed them out only to find out I was unable to keep up on the monthly payments. I’m 26 now and have no active credit cards. I have heard that after 7 years the debt comes off your credit report. If this is true, some of these debts will soon be coming off.

I am considering my options. I could file chapter 7 bankruptcy or I could start tracking down all of these debts and paying them off one by one. My main goal is to repair my credit within a few years. I know filing bankruptcy will severely impact my credit but will bankruptcy look worse on my credit than having unpaid debts from years ago that are settled out/paid off?