Why is state-space representation more numerically stable than zeros-poles representation?
This is because polynomial root finding algorithms are terrible without any implication that people code it wrongly or else. It is an ill-posed problem whereas eigenvalue computations and hence generalized eigenvalue problem solutions are much more stable. 

Any mistake in any of the pole/zero data permeates to all entries of the polynomial entries and contaminates them which in turn causes big numerical inaccuracies in the polynomial root finding. 

Plus, MIMO system representations in both are simply asking for trouble since common terms are very difficult to retain and after a few manipulations you can easily create dummy roots -which could have been considered to be numerical noise- becoming actual modes of the representations. 

Similarly, canonical representations suffer from the same problem in state space. You can test it via creating 2 identical A matrices and perturb the entries of the row/col that holds the entries. Then create a balanced realization of the same system and perturb the A matrix entry of that representation and you'll see that the difference is usually very big.

In your comment you mention the nonuniqueness of the SS representation and it is true. But the dynamics are identical, hence they form an equivalence class up to transformations with nonzero transformation matrix $T$. That's actually a feature not a bug.