So what do you guys think...whose gonna put up more of a fight?

I said giant because he can use tools and think strategically.

A mammoth is sixteen feet tall and weighs twelve ton.
That is a BIG animal.
I don't think there should be many things tougher than them.

It's pretty much Shaq vs Elephant.

I think Elephant would win.

Mammoth.

I think that the giants will be far more challenging to defeat. Yes mammoths are larger, but land dreughs were much bigger than ogres in Oblivion, but because the dreughs were so large, it was easy to dodge between a couple of rocks and light them up with destruction magic. Ogres, on the other hand, while being about equally tough, could maneuver better and were far more challenging in my opinion. Not to mention, you're likely to only encounter mammoths on open plains areas or maybe in forests, places where you can draw the enemy to terrain which suits your combat style. You may encounter giants anywhere, caves, plains, forests, dungeons, ect. and they may have the AI to draw you onto their turf.

I think PC will be stronger than anything else in game.
Suppose you manage to enlarge yourself with some odd magic. How powerful will you be at that point?
Since giants have hands and brains, it'd be fair to expect that some of them will be threateningly powerful in this regard.