I agree with wrk101. If you are willing and able to do the work yourself, most of the bike can be taken apart and refurbished with little more tha degreaser, grease, and elbow grease. You will want to replace the tires whether they need it or not, knobbies are suboptimal for pavement riding. The Detroit Bikes has fenders, which may be useful for your purposes (although you could probably put them on the Schwinn). It also has only 3 speeds, which may or may not matter, depending on the topography of your local terrain.
If, on the other hand, you plan to have the work on the Schwinn done by someone who is being paid, IMO it probably does not make sense.