Equalization and then Sharpening vs Sharpening and then Equalization
Since the Histogram Equalization isn't Linear Operator the order does matter and the result of the doing one before the other changes the final result.
Sharpening would work best when all the Dynamic Range is used.
Hence I'd first maximize the Dynamic Range by Histogram Equalization and then would apply the sharpening.
You might also think of the noise when making this choice.