I can't say it's always been this way, but they are fairly close now, at least for in-state. $339 difference in in-state tuition.
MSU: Cost of Attendance, In-state: $27,241, Out-of-state: $51,068
Tuition and Fees In-state: $14,063 Out-of-state: $37,890
Michigan: Cost of Attendance, In-state: $28,776, Out-of-state: $59,784
Tuition and Fees In-state: $14,402 Out-of-state: $45,410
Yeah. I've heard that MSU's tuition has went up A LOT since I attended in the early 90's