Ryujin
Legend
Depends on what you call "real power". The veto winds up being a *major* point - that which the President does not like, does not become law unless you have serious support in the legislature. This forces the system to have a whole lot of negotiation, and puts the President in a solid position to lead that negotiation - thus, a lot of effective power.
The President can send a bill back for re-vote, if I understand the process correctly. Given the adversarial nature of your government that will almost certainly kill it, in practice, but the theory is to force a re-think.
The Prime Minister of Canada is in charge of the process from inception, to signing into law. He leads the party in power. When comparing the levels of power in their respective governments, the Prime Minister has far more power. Note that I'm not saying that's a good thing.