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).

A new construction window does not always mean more glass. It depends on window type and size and manufacturer. When we replaced our old leaky Aluminum windows with AL clad, wood interior windows (Marvin Ultimate), we ended up losing about 6+ inches of glass. The old aluminum had skinny sash while the new ones have large wood pieces inside. The large wood pieces did not affect the views as we feared but they certainly did not yield more glass. There are several reasons to stay with replacement even when changing siding and trim. We lived through this in our previous house. When trim around the windows is expensive to replace and already matches the house trim. WHen original frame is sound and we are not changing window size. When replacement window is sufficiently better than old window. When project cost of new construction is way higher than replacement windows. WE ended up using replacement windows for our previous home. For our current house, the trim was bad and needed replacement anyway, the framing surrounding the windows had visible water damage and there is no replacement for those poor quality Aluminum windows. The end result was new construction windows.

Not being "like for like" does not necessitate new construction. You are dealing with an empty opening whether you are installing into a buck frame or a rough opening. Replacement style is a nice choice for most people. New construction (full tear-out) is a better choice when you have existing water management issues, substantial structural frame damage/rot, or you are very concerned about the potential loss of glass area. The pros of replacement are cost ( typically a couple hundred + ), your interior woodwork is not disturbed, and a far less intensive installation. Did I mention that there is a MAJOR cost difference? ;)

Replacement windows are just that - the sashes ( using a double hung window as an example) are removed along with the jamb liners, leaving the frame of the old window, and a new window is inserted. Picture a frame within a frame A new construction (or full tear out as some call it) is where the entire window is removed right down to the studs of the house. A new construction window will have a flange that is called a nailing fin that is nailed directly to the sheathing/ studs from the exterior. All three of the manufactures you mentioned do make windows for both applications. In most cases a new construction window is not needed, unless of course there is great deal of integrity issues with the frame of the window you are replacing. Additionally, a full tear out job will generally yield more glass area. You mentioned three manufactures - two that make vinyl, and one that makes fiberglass (ultrex). Very difficult to rank from best to worst with these three, as they are all top producers. The difficult part of the ranking - you would need to determine if you want vinyl or fiberglass first. If you decide vinyl - you are in luck....you are right in the heart (Ohio) of a number of good manufactures.