As a Sales Director, Is it better to make competition between sales teams? or it is better to work as one team to get your target?

Both.

Friendly competition between sales teams is good: it helps encourage people, keeps them motivated, and it's fun. 

But never forget that the real target - the one the shareholders care about, and the one that pays everybody's salary - is "total sales".  Nobody outside the sales department cares about the different sales teams.  

This distinction can be implemented many ways.  For example, have weekly sales targets for each team with fun or trivial prizes or penalties.  However, the monthly target, which is used for bonuses, is for the whole sales department. 

Compition must be healthy between sales teams. Cordination must be there betwwen two teams. As well as distribution of customers too. Some times the mixing of same customer gives a bad impression of your company to the prospect, if the sales member of both teams visiting one customer same day. Just imagine how the prospect will respond about the company management.

as a sales directors they should work as a team for a better results

Working as one team gives good Result

As per my experience over the years both type of strategies are good depending upon the situation at hand. There can be instances whereby a competition between the teams can produce better results. It is the responsibility of the leader to ensure that the competition is healthy in the best interest of the organization. By having a competition between the sales teams it becomes easier to cover a larger area and contact a bigger clientage number wise. However there can be a situation whereby a dedicated and cocerted effort is required to focus on a particular area or specific clients, in such a scenario one team is more effective and can get to the target more easily and in a shorter period of time.

It should be both depends upon market situations, performance, friendly competitions.