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. . . is larger? (area)
Michigan: 97,000 sq mi
Ohio: 45,000 sq mi
Yes, a lot of Michigan's area is water, but even if you only count land area, it's still ahead.
. . . has a greater population?
. . . was admitted to the union first?
. . . is the birthplace of more 20th-century presidents?
McKinley, Taft, and Harding were born in Ohio. No president has ever been born in Michigan. (Ford was born in Nebraska.)
. . . has the larger largest city?
. . . has the larger capital city (metropolitan statistical area)?
. . . has more cities with population greater than 1 million?
. . . has the higher highest point?
Mount Arvon: 1,979 ft
Campbell Hill: 1,549 ft
. . . has the taller tallest building?
Key Tower (Cleveland): 947 ft
Detroit Marriott at the Renaissance Center: 727 ft
. . . has the larger national park?
Isle Royale: 571,790.30 acres
Cuyahoga Valley: 32,571.88 acres
. . . has the longer river that shares its name?
Ohio River: 981 miles
Michigan River(Colorado): 69 miles
. . . has the larger lake that shares its name?
Lake Michigan is 22,404 sq mi. There is no significant lake named "Lake Ohio" (or "Ohio Lake").
. . . "won" the Toledo War (by getting Toledo)?
. . . has more wins in the University of Michigan-Ohio State University football rivalry?
Despite Ohio State's recent dominance (15-2 since 2001), Michigan still leads 58-50-6.
. . . has won more NFL championships?
The Cleveland Browns and the Detroit Lions have 4 each, but Ohio also claims championships by the Canton Bulldogs (2), Akron Pros, and Cleveland Bulldogs. Neither state has ever won a Super Bowl.
. . . has a more recent World Series win?
Cincinnati Reds: 1990
Detroit Tigers: 1984
. . . has the highest ranked university (according to U.S. News and World Report)?
University of Michigan: #25
Case Western Reserve University: #40
. . . has a greater percentage of its population employed in manufacturing?
(both states are Top 5 in the U.S.)
. . . is closer to Toronto (as the crow flies)?
Conneaut, in the NE corner of Ohio, is 131.95 miles from Toronto. Port Huron, along the Canadian border, is 160 miles from Toronto. These may not be the absolute closest possible points, but I am confident that no point in Michigan is closer than the closest point in Ohio.
. . . has a town named Hell?
And one called "Bad Axe," too!