My original roof on my home is approx 19 years old.It probably needs to be replaced.One roofer's estimate recommends a tear off and replacement of the asphalt shingles (more expensive)the second one says that is not necessary just cover old roof with new shingles.
What is best other than price difference.Both insist there way is best .

Of course we can't see the condition of the old shingles.

And how many layers of old shingles are on the roof. Most cities ( states) have building codes when you go get your building permit to do this, and yes you will most likely need a building permit to re-roof your home.

Most codes allow two or three layers of singles. So if you only have one and you don't have a lot of bubbling of the old shingles normally there is no problem and I put two layers on all the time.

Because of many issues I don't personally believe in putting three layers on and normally tear off if there are already two layers on.

You can not see any wood damage to the actual roof if you don't tear off. But if you have a attic area the actual roof should be inspected to be sure there is no rot or damage to the roof itself that could or should be fixed when you are getting ready to re-roof.

Code permits a second layer of roofing. May as well go with the low bid. If you still own the house in 20 years, you can pay the tear off price then.

Have you considered replacing it yourself? It is not rocket science. It is a lot of work, but you can shop for roof top delivery of the shingles. Others here and I can help you make a nice job of it.