I'm sure Mises himself observed the real world economy when he came up with the business cycle theory. So it seems that for Austrians empirical observations are just as important as for the mainstream economists. The business cycle itself can be considered an economic model.

Therefore can you please explain why Austrians don't believe in models? Maybe I don't understand what exactly Austrians object to, because to me it seems that business cycle itself is a model.

What Austrians don't believe in are models that can be completely expressed as a set of equations. The problems with these models are

A) Just like those equations you see in physics books, they make initial assumptions. The reason these intial assumptions are made is because otherwise the math involved will be difficult, if not impossible, to solve.

In the physics models, the assumptions are realistic. For example "For small values of X, sin x can be approxiamted by X". Or, "We can get a rough approximation of what is going to happen if we assume lack of friction".

But when it comes to economic models, Austrians claim that the initial assumptions are unrealistic to the point of absurdity.

B) The models assumes that people always do the same thing, just as particles do in a physics model. But of course this too, is an absurd assumption.

So much for the models AE rejects [or more precisely, what I know of this subject].

AE models differ in that they are built on assumptions that anyone sees are valid, and use rules of logic that are universally accepted to make their "model".