For me, being directive is saying "do the things that I have told you to do" and supportive is "do what is best for the company, and if you have problem I will support you." To be an effective project manager, which is more important, to be directive or supportive?
Both. Team maturity, process maturity, experience, risk, stakeholder support, and many other variables dictate the type of leadership and management approach you need to deploy. And you can expect to change your approach as things change.
Generally, avoid trying to find a single answer comparing two extremes. Our world is way more dynamic and random than that.
Actually, the most effective leadership style is the one adapted to the level of competence that a group or individual has regarding a specific task.
Hersey and Blanchard have described this in their "Situational Leadership Theory".
Competence is a combination of having sufficient knowledge or expertise as well as the motivation to do the job. For instance, a highly skilled programmer will not be very happy if he has to spend many hours doing helpdesk.
So, depending upon the 'situation' (skilled or unskilled vs motivated or not), a leader should adapt his management style accordingly. Hersey and Blanchard identified four styles:
- Telling: the most directive
- Selling: while still directive, there is more effort in convincing the employee
- Participating: both leader and direct work together to find the best approach
- Delegating: this gives the highest autonomy to the employee
Your approach towards a specific employee (or team) can change over time depending on the employee acquiring more knowledge about the task, or switching to a task he is already confident with.
There is a well known chart (an example can be found here) that summarizes the relationship between the styles and how you can move from one style to the other.
Cultural Expectations vs. Role Effectiveness
Whether a project manager is expected to be a command-and-control authority figure or a servant-leader, coach, or referee is largely a matter of organizational culture. The expectation the role is generally set by the executives to whom the project manager reports; you can often be guided by their management style in determining the cultural expectations, but it's generally better to have it spelled out explicitly.
Of course, a better question would be: "Which style of management is more effective?" Unfortunately, there's no canonical answer to this question. Agile methodologies like Scrum typically require servant-leader, coaching, or referee-style management to fully enable the self-organizing principles of the Agile Manifesto. Other methodologies may lean towards other management styles.
I'm unaware of any canonical research that makes one type of management better than the other under all circumstances. Therefore, it is up to you (and your development and management teams) to determine what works best in your specific organization. The important thing is to make sure everyone in the organization is on the same page, and that everyone agrees on the nature of the project management role.
As some of the other responses state, the answer is "both". Keep in mind that your job as a Project Manager is to maximize the effectiveness of everyone on the team.
The stronger team members will know what they're doing and you probably should stay out of their way. Encouraging them and praising them for their accomplishments is the correct approach.
You will have other team members who are challenged, whether it be because they are new to the organization, new to the technology, or perhaps not a good fit for the role. For these folks, you should be directive -- provide them with a detailed set of instructions for the work they do.
I'm of the opinion that as long as someone has a positive attitude, its up to his or her manager to come up with an environment that maximizes his or her contribution. In some cases this means you should be "supportive" while in others it means you should be "directive".