When you're thinking about changing the windows in a house, you need to make one fundamental choice: whether to slide the new window into the old window frame (the first photo), or whether to remove the old window right down to the structure of the house (the second photo) and replace the whole thing.
You will always get a better job if you remove the old frame because it will allow the installer to check for any moisture damage, to provide a drainage layer behind the weatherproofing, weatherproof it from the outside with caulking, totally insulate the cavity, and finally seal it all air tight on the inside. Sliding a new window into an old frame rarely gives the same trouble-free and energy efficient results, but, on the other hand, it is faster and cheaper to do. Removing the old frame also allows for more glass area, because you are not doubling the framework. The only time leaving the old frame is really justified is when it is an old historic building and the woodwork could not be easily replaced.