Depends on how bad of shape the frames are in and how many windows you have. Replacements are going to cost less because the labor is more to do a new construction install. OTOH don't let them talk you into replacements and leave you with the possibility of water penetration or not addressing all the potential rotted wood.

I'd try to stick with new construction, if you can afford the installation costs. There is usually minimal difference in the cost of the windows. It is more invasive, therefore more costly in install the new construction type. I'm in complete agreement with you concerning the integrity of the existing sills and frames.
Good luck and let us know how it all pans out.

I know what your probably going to say, but what kind of windows do you have now (wood, aluminum etc) and what kind of exterior is your house (brick, wood, vinyl etc)?

Everything is wood. The exterior is shingle. The contractor's think probably absteosis. I have some extra shingle from the prior owner. Also, the contractor said if that runs out he can use cement board for the time being until I side the house. Which I anticpate within the year. I understand the cost differential between the two, but if I can swing the additional $1000-$2000 to get the benefits of new constuction windows isn't that worth it? Or am I missing something. Financial this is a one shot deal. Can't afford to have issues 5 yrs down the road and then have a contractor tell me he needs to redo the window, because rot and water damage.

Rotted sills are pretty commonplace and most of the rot that people see is often times draining behind the exterior cladding of the home and therefore not rotting structure. You need to take a closer look (i.e. remove some exterior cladding and inspect structure or remove the sill and take a look at the rough opening).

While the rot may look significant, a majority of what is out there is non-structural and therefore does not require a full tear out. If you go full tear out, you absolutely should use a flanged/new construction window.

Having asbestos siding certainly complicates matters a bit and you would be well advised to check code requirements as it pertains to that specific ACM (Asbestos containing material). There are more stringent requirements if the material is removed professionally (i.e. by a contractor) as compared to the homeowner (not all together dissimilar than the RRP fiasco).

+1 you should remove some siding and cladding in the area of a window or two that show some signs of rot. See if it is beyond the window framing and into the structure of the house. Base your decision there.

If the contractor or you decide to go with New construcion, he is going to have to remove some trim on the extior to get an accurate measuere anyway. At least that is how we do it.