I've always thought that all of the separate Bijuu would represent different elements. Sukaku is Sand, Kyuubi is Chakra etc. I'd like to see the fire one.

I've been sitting on the following for a while now, but I'm just gonna throw it out here, so you guys can rip it apart/slash praise it and give me free stuff.

The only two Jinchuuriki we've seen are Naruto and Gaara. They were both made Jinchuuriki in slightly different ways, or for with slightly different intents. Naruto was made a Jinchuuriki to seal away the Kyuubi and to give Naruto the power to protect himself if necessary. Gaara was made a Jinchuuriki in order to be a weapon for the sand, Gaara was supposed to be able to wield this power at will.

This, I think explains the fundamental difference between them: Whereas Naruto has to willingly access the Kyuubi's chakra, Gaara has access to Shukaku's sand powers all the time. One thing they have in common is that both Naruto and Gaara are able to deflect attacks against them using their Bijuu's elemental power. Both of them also have a form where they become wrapped in an armour of their element, and grow a tail(s).

Gaara, as we've seen is able to completely release the Shukaku; he becomes wrapped in sand to the point where it transforms into Shukaku itself and Shukaku's personality take over. In the first episode in the series, the Third made the comment that Naruto, using the forbidden scroll, could completely unseal the Kyuubi.

I know that two people aren't enough to prove anything, but I think that if another Jinchuuriki shows up in the story then they will show the same characteristics. At first, having an innate relationship with their element (whether consciously (Naruto) or unconsciously (Gaara)) and then being encased in an elemental armour with increasing numbers of tails.

Edit: About the Kyuubi, the legend I heard was that a Kyuubi was the oldest and strongest Kitsune (shape-shifting fox demon). Kitsune gained tails and power as they aged and were usually seen in mythology as having either 1, 5 or 9 tails. This was Japanese mythology though.