Different Character Movement on iOS

I am currently trying to make a little Platform game for iOS. (This is my first Game.)
I have developed the following code to move the main Character.

void InputCheck ()
		{
				Touch t;
				bool tOk = false;
				if (Input.touchCount > 0) {
						t = Input.GetTouch (0);
						tOk = t.phase == TouchPhase.Began || t.phase == TouchPhase.Stationary;

				}
				if (Input.GetKey (KeyCode.Space) || tOk)
						inputJump = true;
				else
						inputJump = false;
				if (longDead  inputJump) {
						resetLevel ();
				}
		}

		void Move ()
		{
				if (characterControler.isGrounded) {
						moveDirection.y = -1;
						if (inputJump  !dead) {
								moveDirection.y = jumpPower;
						}
				} else {
						moveDirection.y -= gravity;
				}
				if (!dead)
						moveDirection.x = speed;
				else 
						moveDirection.x = 0;
				characterControler.Move (moveDirection * Time.deltaTime);
		}

The Code works just fine in Unity, so i builded it for my iPhone and tested it.
On the iPhone, the Character jumped much higher and run much faster.
Does anybody know, why there is such a big difference between the Player in Unity and the original device?

Stuff i used:
Macbook Pro - newest OS X
Unity - 4.3.4f1
Xcode - 5.0.1
iPhone 5s - newest iOS

You need to set a constant frame rate, try this way: Unity - Scripting API: Application.targetFrameRate

Thank you for the quick help, it worked!
I thought (moveDirection * Time.deltaTime) would be enough …