The answer to this question might be one based on subjective experience. From my point of reference, determination is important because it helps to give focus to consciousness. Individuals with determination help to better understand what has to be done. In a way, determination helps to address Tolstoy's dilemma regarding what it means to be human. Tolstoy argued that all endeavors must seek to answer two fundamental questions: Who we are and what shall we do. These two questions are answered by the presence of determination in our lives because it helps to give structure and purpose to what we do and how we shall live. In this light, I would say that determination is highly significant to our lives.
Consider Glasser's Reality Therapy. Basically, he says determination to make one's quality world a reality is the sole determinant for behavioral change.
Essentially, if humans are bored, lonely, angry, or in any other place that is emotionally undesireable - Glasser (and others) say that determination to get out of this undesirable spot is essentially what gets us out. Now, people who suffer from many years of habitually attempting to change their outcome the wrong way - may be determined to change, but never do. This is where goal setting comes in - and often therapists or counselors (or teachers or loved ones) must intervene to help the individual not only paint an attainable quality world picture - but achieve it by making the right choices.
I think that there is no doubt that determination is the thing that does the most to affect how much we get out of the talents and opportunities that we are given in life. I think that a person who is determined will generally be more successful and happier than a person who is not.
Of course, a person who is more talented or richer may end up "ahead" of a person who is more determined, but less lucky. But I think that determination can make up for a relative lack of talent or wealth.
I also think that a determined person will be happier because he or she will not have the feeling that they have wasted their opportunities and talents.