I think there are 'old aircraft' and old aircraft. A 767 is an example of the former, whereas a Caravelle would be an example of the latter. Aircraft undergo stringent inspections every x hours, have to comply with Airworthiness Directives (ADs), and even more stringent standards and practices as far as maintenance goes. That's even truer for commercial airliners. So the chronological age of a plane is usually not a great indicator of its true state.
For example, I prefer flying on a 757 to a 737, even a new one, despite the fact that 757s are no longer produced: they have fantastic performance, and a well-maintained 757 is a very good plane to fly in, despite its age. Ditto for the 767. It's a beautiful twin-aisle plane, and I recently flew on one from Atlanta, and loved the comfortable ride. In fact, I was overjoyed to discover that I'd get another opportunity to fly on a 767, having flown on one to Hawaii (Hawaiian used to operate 767s also) some years ago. I would prefer flying on an (older) 767 to even a 757. If the airline does maintenance properly and has a good safety record, then it's actually better to fly a older airplane because it is likely to be more comfortable, powerful, and safer.