Inserting a window into a existing vinyl frame does not work so well. The existing frame should come out and a new window with fins or without could be used.

Do you by chance, have vinyl windows installed in stucco?

Some pics would be helpful here. As Todd mentioned, you really can't do a true "insert" and put a new vinyl window into an old vinyl frame. More than likely the contractor is offering two methods with option being downsized to fit inside the jamb ext/return, this would be less invasive and more of a "replacement" install. Your woodwork would indeed be preserved, a new interior stop (typically shoe or cove) would be added to cover the edge of the window.

Regarding glass loss, that is heavily dependent on the window coming out and the window going in. Some are much slimmer than others. If all were equal, you can look at the fact that the new window would be downsized roughly 3/4" on each side for reference, but again that could be more or less based on product. I'll say this, its a very common method of installation and very, very rare to get a complaint about glass loss unless you have small openings to start.

You might even gain viewable glass depending on the windows you hAve and how they measure and install them . Ideally they would out in the same size window.

a properly installed replacement ( insert ) will work just fine.

I would not call this a true “insert“ job. The existing vinyl frames should come out regardless . The depth of the existing frames and if there is any existing Exterior window trim would determine the best installaction method, or the most cost effective installation. Insert vs full frame gets a little muddied sometimes and id say you need at a minimum a modified insert install or a true full framed install. With out the opportunity of being there I am merely throwing out vague ideas on how I would tackle the situation .