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From the point of view of getting rid of the big blind, obviously a bigger raise will be more effective. However, my experience is that the difference is very small. If they have garbage, they will throw it away in either case. If they have a good hand they will play. There a few intermediate strength hands that they will play against the miniraise but not against the big raise. However this is not a horrible thing because these hands are on average weaker than my average raising hand, and I have position on them.

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Do you really want to see a miniraised flop in position against 22-77? In my opinion small pocket pairs are why it's so important to raise big with your big hands. With AK, you want to be able to play a flop like A-2-6 very aggressively, and you simply can't do it with the same assurance if the BB was able to limp in for less than a tenth of his stack.