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This is a broad question and is not easy to answer.
A major difference is your philosophy.
Kanban (if implemented correctly) is pull based system.
Min-max is still looking forward i.e. it looks at your current onhand, future demand, future supply and then comes up with a requisition.
But there are no hard rules.
Min-max works well when the issue from subinventory is not bucketed. But in a shop floor type of situation, you may have an operator going to the RAW inventory to get a bucket of screws.
If you ran min-max on the WIP subinventory, it will think that you have plenty and won't generate a requisition.
But another operator may require those screws and he may be out of them. In this case, a Kanban will work better because as soon as the first operator took the last nth bucket, Kanban would have triggered the replenishment process.
Kanban requires you to spend some time analyzing your issues to come up with right number of bin sizes and number of bins.
The thumb rule is that Min-Max is simpler to implement.
Kanban is a little more involved. So if your organization is not mature enough or requires a simpler solution, min-max will work better.