Personal streams:

For players with their Twitch account linked if they are live on Twitch and in a match it could list them in a separate list from the regular streams and give cool info like stage bans and opponent and stuff. Like have a page with the match and stream integrated. Could also put that they are streaming whenever their Twitch is live on their profile page and player card. Possibly integrate Twitch chats into chat somehow like IRC chats are. Also if someone is streaming and searching maybe a Twitch icon somewhere in their search. 

Tournament streams:

Marked as live on tournament listings. Listed separately in the streams. Maybe even put a red exclamation point thing on the streams tab if one is live. Point is basically to advertise them. Maybe host them with the official Twitch sometimes. Tournaments get the site advertisement on Twitch and also help create a competitive and exciting environment and generate hype. 

Official stream:

Used for ladder sponsored tournaments and stuff. If live it should be clearly and obviously indicated on the chat page somewhere. Like a Twitch icon at the top right with a red exclamation point thingy. Possibly let tournaments apply to stream on it. Btw ladder sponsored tournaments. Like "Smash Ladder East Coast Melee Netplay Fall Invitational" or "Smash Ladder European Smash 4 3DS Winter Open" and throw sub for prizes. Also throw achievements and access to special flairs.