There is skepticism and probably a valid one on people moving across companies of very different scales in their career. If moving across companies of similar size is like a move from a city to a city within same country, moving across companies of dramatically different size may be more like immigration to a new country speaking a new language with a different culture.
A generalization of differences based on company size is an invitation to different opinions at best. How about these?
– Most companies using email, and often MS outlook email. What would you say of the company size if outlook is using “first name” to locate people versus “last name”?
– Companies have news travelling so fast, that whatever news you share upstairs, it would be known downstairs before you finish walking downstairs. Does this sound more like small company or a fortune 500?
– Is Gossip more common in small companies or big ones?
– Pace of work – many would say pace of work is faster in small company, I think a fast pace in a big company is like running fast with tons more consideration and a few pounds of weight on your feet. If one can achieve things in a fortune 500 companies, probably the person can handle the pace in smaller companies.
– Big Minds, Small Minds. Where do you find more people with bigger picture?
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Sometimes, small companies hire folks with experience in big companies. The idea could be that new folks, with big companies’ experience, could add scale, structure and process to facilitate growth. Unless there is critical mass of new hire in senior enough positions, such a hiring strategy could backfire. The new folks could find themselves going backwards because things in small companies tend to be achieved with varying qualities, through relationship in lieu of process; and change control process or change management process may not be easy to pull off.
oliviatamccue 
This is getting to my heart! Although I am yet to start my new job, the various considerations mentioned have crossed my mind many times already. Fingers crossed, I await the new start with hopes and anxieties at the same time.