Your question is somewhat bigger than you might think.
Quote:
What is the better strategy overall min or shove?
What is the better option for my hand min or shove?
These two questions are very different but equally important to understand.
Min raising as a strategy will generally be more profitable because we can open a wider range and take advantage of more +ev spots.
Sometimes we will find spots that, in a vacuum (not worried about regs), will be more profitable to shove than min raise.
We can find these spots by comparing min raising vs shoving in an icm program.
There is sometimes medium strength hands that do slightly better as a shove than a min raise, but usually min raise opening will be the superior strategy.