Who has greater control over Canada's military: the Prime Minister or Governor General?

Symbolically, it the GG. Realistically it's the current PM and his cabinet.

The Prime Minister has control. He or she is the one that was elected by the people and carries out his or her government's mandate. The GG is essentially a figure head, representing the Queen, in Canada and has very little if any power in the running of the country.

the museums . thats where all our tanks etc... are . ;-)

The Governor General. The Prime Minister is not a commander in Chief.

I'm not Canadian, but my understanding is that the Governor General, in her capacity as the representative of the Queen, acts on the advice of the Ministers on pretty much every major decision. I would assume that includes the military.
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I know that in Denmark, the Queen's acts are not valid unless they're countersigned by a Minister (who is an elected official and Member of the Folketing, or Parliament).
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But I'm not sure how Canada handled that issue other than that it would be different there than in the United Kingdom since Canada has a written Constitution and the U.K. does not.
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Thanks! That should be fun to look up. Interesting question. +5

The Prime Minister controls the Military, the Governor General is mostly there to act as a figurehead representative of the Queen, since we've repatriated our constitution.

Neither. The US military has more influence over the Canadian military than any political figure, more's the pity.

Evidence - Avro Arrow and CF-18.