Counter before or after noun


When I first learnt about counters I was taught that the number with its
counter comes after the noun e.g.

> 鳥を二羽見た。
>
> I saw two birds

Recently I've been seeing constructions like this:

> 二羽の鳥を見た。

Is there any difference between these two constructs and any reason I should
choose one over the other?

