> Question: Which parameter is suitable to indicate how "good" the
> measurement fits to the Kalman filter?

To estimate a quality of association you can use *likelihood function*. The *likelihood* considers not only *residual* but also *uncertainty* and represented as scalar value:

$$\mathcal{L} = \frac{1}{\sqrt{2\pi S}}\exp [-\frac{1}{2}\mathbf y^\mathsf T\mathbf S^{-1}\mathbf y]$$

> Problem: For an object tracking scenario with multiple objects and
> multiple tracks, I want to choose the "best" assignment
> object<->track.

The question which you are interested is called *data association* and as was said there are a lot of solution and this question is too broad. Here are some of methods (you can google it and find more information):  
 - Global nearest neighbour (in Euclidean space);  
 - Global strongest neighbour;  
 - Joint probability data association;  
 - Multiple hypothesis tracking (the best choice).