Both materials work in Chicago. They ask different things of you, and they suit different houses. Here is the honest comparison.
Lifespan: commonly a couple of decades or more in residential use, depending on the product and the installation.
Maintenance: low. Wash the frames, keep the tracks clear, check the weatherstripping. No painting.
Chicago weather: handles freeze-thaw cycles and lake-effect moisture without rotting. Colour choices are limited and the frame cannot be repainted later.
Cost: generally the more affordable of the two for a comparable size and configuration.
Lifespan: can last a very long time when the finish is kept up, and individual parts can often be repaired rather than replaced.
Maintenance: real. Expect periodic painting or sealing, especially on exposed south and west elevations.
Chicago weather: performs well when protected, but standing moisture and neglected finishes lead to rot. Clad exteriors reduce that risk.
Cost: usually higher up front, and the maintenance is an ongoing cost of ownership.
Vinyl tends to make sense when you want low upkeep, standard openings, and a sensible budget across a lot of windows. Wood tends to make sense on period homes where the sightlines and interior finish matter, or where a block has a consistent look worth keeping.
A well-installed vinyl window will outperform a poorly installed wood one every winter. In older Chicago openings that are out of square, how the window is set, insulated and sealed decides how it performs. That is worth more of your attention than the material debate.
Call and describe the house. We will tell you what usually works on that type of opening.
No forms, no waiting on email.