What the numbers mean
A $75,000 salary in Chicago gives you the equivalent of $60,254 in purchasing power after accounting for state income taxes (5.2%) and the local cost of living. The same salary in Nashville gives you $65,789 — a difference of +9%.
Median rent in Nashville runs about $1,600/month — roughly $100/month less than Chicago's $1,700. That's $1,200/year back in your pocket before you factor in anything else.
No state income tax in Nashville. On a $75,000 salary, that's roughly $3,900/year you keep that you wouldn't in Chicago.
These numbers use a cost-of-living index where 100 = national average. Chicago's index of 118 means it costs 118% of the national average to maintain the same lifestyle. Nashville's is 114.