Unity animation identical to Cocos2D animation not smooth?

With this question, I refer to a Cocos2D animation I recreated in Unity that looks not as good as it does in Cocos2D's version.

It's a simple pull up menu. It shows it's top at the bottom of the screen and when clicked it moves up to reveal a menu structure. With cocos, it's a simple CCEaseExponentialInOut function, starting slow, getting fast and slowing again at the end.

It looks very smooth on an iPad.

I recalculated all values, frames, and positions to do the exact same thing in Unity with the animator and the curve editor. But here, the animation doesn't look smooth. I can't even tell what the exact difference is, I tried to record both versions with Quicktime, but it's not fast enough and therefore both recordings look nearly identical when it comes to the menu position within the frames.

I don't understand this, I tried it with Unity in a completely empty scene and still it looks like the refresh rate is too low? I'm sorry that I cannot provide any more info, because all the numbers are identical and it's just "not right" to look at.

Does anyone have any advice on this, or encountered this problem too?