when is the best time to play Dragonborn?

Is it before or after defeating Alduin?

It works a lot better after, imo.

And why is that?

you don't sound like such a wuss when Miraak talks to you.

Before Alduin's defeat; Miraak basically insults you for only killing a few dragons

After Alduin's defeat; Miraak compliments you for defeating Alduin and then starts bragging about himself.