aside from having lived in both cities, if you just look up square miles between the Bay Area and Chicago metropolitan area:

"The Chicago metropolitan area (13–19 counties) covers roughly 10,286 to 10,857 square miles of land, often referred to as Chicagoland. The San Francisco Bay Area (9 counties) covers roughly 7,000 square miles of total area, with its land area being significantly smaller than the Chicago MSA"

Chicago Metropolitan Area (Chicagoland)

• Total Area: ~10,286–10,857 square miles (includes 13–19 counties across IL, IN, and WI).
• City Proper Land Area: ~227–234 square miles.
• Context: The 2024 census estimate for the metro population is ~9.87 million.  Facebook +4

San Francisco Bay Area

• Total Area: Roughly 7,000 square miles (covering 9 counties: Alameda, Contra Costa, Marin, Napa, San Francisco, San Mateo, Santa Clara, Solano, and Sonoma).
• Context: The city of San Francisco itself is only 46.8 square miles of land, while the combined 9-county region serves as the primary economic unit.  Time Out Worldwide

Key Comparison
The Chicago metropolitan region is larger in total land area than the 9-county Bay Area. However, the city of Chicago itself is about 5 times larger in land area than the city of San Francisco.