Bricks, Masonry, Asphalt and Concrete - Repave or replace asphalt drive way

A company will charge $2000 for demolition and new asphalt drive way. He will instead charge $1000 to just repave it. The drive way is about 10' x 22'. It has a lot of little cracks and one about 2 inches wide. There are two small sink holes. There are no pot holes. Is just repaving a decent option and will that even out the surface and last a few years? Will it strongly adhere to the existing surface?

To add to my comments in your other post, I am not familiar with your local prices.

The sinkholes I'd consider a problem! What is the cause? Drainage or poor soils underneath? Unless you have the old stuff dug up you won't know.

New asphalt will stick to the old stuff nicely and the old stuff would provide a strong base if it wasn't for the sinkholes. Also note that if you have a new coarse of asphalt put down, it'll likely be very thin in spots in order to blend with your existing grades and thin coarses inherently will not last long.

So my recommendation is get the old stuff dug up, have the sinkhole problem(s) fixed, and have a new driveway put down that is of uniform thickness all over.

you have potholes because you have weak or nonexistent base under the drive. you could have them add base material in the potholes and do a 1.5" overlay and get several years out of it. make sure they use tackifier between the old and the new.
if you want a longer term fix, have them excavate the area down enough to get at least 4" packed base before the lay the hot mix.