So I have a 17 year old furnace and AC.. not broke yet but have been doing some research. Here is what I found:
Your furnace is likely 80% efficient range. A new furnace would be 95-99% efficient (meaning 80% of gas it burns heats your house). The math does not work out EXACTLY like this, but in general your heating bill could be about 10-20% lower with a new furnace. If you spend $100 per month heating x 6 months a year, you would save like $60-$120 a year in gas. Nothing to sneeze at, but you won't get back the money you spent on a furnace (5k+) in a short time.
On the other hand, old central AC units were really terrible. You are likely at something like a SEER of 8, where a new unit would have a SEER of 14-18. If you AC for 6 months a year at an average of $300 a month, this could save you $900 a year in electric - which would be a VERY fast payback of everything. But if you hardly use your AC, it won't do much.
So in summary:
If you are a big AC user, and have 5-12k to spend, replace EVERYTHING with a high efficiency model. Will pay for itself in a few years, and last for many more years.
If you are not a big AC user, see what you can do to patch it up. Maybe shop around and get different quotes, maybe you can get it fixed it for $500 from someone else. But realize your AC and Furnace were built to last about 15 years, they are not going to last forever. In the next 2-5 years you should plan on replacing them.