Which leads to greater character diversity: more options or fewer? There are several moving parts there: the number of choices, the number of options for each choice, the importance of those choices, and the ability to change them. I should note that I will be considering the majority or the people who care; there will always be people in the tails of the bell curve who are trying to make the worst possible choices because of contrariness or a character concept.
The importance factor seems the easiest: the more important a choice is, the less likely there is to be diversity. If something really really matters, there will be one best way to do it or a few best combinations; even if you give me more options for that choice, anything less than the best means gimping the character. Contrarily, if the decision has no practical importance, the distribution will be random, and more options will lead to even greater diversity.