We can define assertiveness by placing it on a continuum between passiveness and aggression and making a contrast with them.   Assertive behaviours reflect the sense of personal worth that the individual has for himself and for the other person.  When we are Assertive we are honouring and reflecting our core values in whatever situation we find ourselves.  We stand up of these values and defend them in a manner which is inarguable.
Looking at the differences in behaviours and attitudes shows some very obvious differences.

Passive Behaviour:
People who typically behave in a passive or submissive manner are demonstrating a lack of respect for their own values, needs and rights.
Many passive people do not express their honest feelings, needs, values and concerns. They allow others to dictate to them, denying their rights and ignoring their needs.
The body language of the passive person is bowed and bent, submissive and non threatening.
Their speech is peppered with "Sorrys"

Aggressive Behaviour:
People who typically behave in an aggressive manner express their feelings, needs and ideas at the expense of others. They need to win arguments. They tend to overpower other people.
The body language of the Aggressive person is threatening , finger pointing, stand over.
Their speech can be loud abusive, rude and sarcastic

Assertive Behaviour:
People who typically behave in an assertive manner use methods of communication which enable them to maintain self-respect and gain satisfaction of needs without abusing or dominating others.  They stand up for their rights and express personal needs, values and concerns in direct and appropriate ways.

The language of the assertive person is riddled with "I talk"
Eg "I hear what you say and I believe that….."
"I recognise that you are upset, what do you need to have happen…?"
"I feel that the time is right to make this change"
"I am confident that when we have covered of the agenda items we will have an agreement"

The Aggressive style gets results in the short term, and breeds an atmosphere of "submission under duress". In leadership styles this styles certainly has an impact , often delivering above budget results and leaving a beaten and demoralised staff behind to be inherited by the nest leader.
The cost to an organisation of this leadership stye is usually not felt whilst the leaders is in position, except perhaps in staff turnover statistics, it is usually felt in subsequent years, after the person has moved on.