Massively overgeneralizing of course, we can observe the following tendencies: Small organizations tend to value people who are highly responsive and who can work independently in a fairly unstructured and unconstrained operating environment. They tend to value people who can do "whatever is technically necessary" to rapidly solve problems and move the business forward towards it's goals.
As organizations grow, such forward progress is easily stymied and halted by interruptions and context switches from colleagues, and velocity becomes largely a function of how much such "frictions" can be reduced or eliminated. Behaviours and traits which were highly valued and rewarded in a small-organization context (e.g. highly independent problem solving and proactivity) can, under many circumstances, become liabilities in large organizations if they interfere with the smooth running of established processes, or cause disruption and confusion to large numbers of people. Reliability (and above all predictability) become far more important than responsiveness or (sometimes) raw velocity.
Needless to say, being able to adapt behaviours and attitudes depending on context is an exceedingly useful skill, and just because you were rewarded for acting in a particular way in a small organization does not mean that you will continue to be rewarded for acting in a particular way in a big organization. The two are completely different beasts, and it's the communications structure that drives the shift in values.