If you work for the big company and professional company you are only a small link of a chain, your work only focus on a very small and specific function in the company.
If you work in the small and new company you will take care a lots of things even from A to Z, you have the opportunity to learn and know everything about the company, your managing skill & flexibility are improving significantly.
So which one I should choose to work for ?
My answer is both but your answer may be different from person to person
If you want to a stable job and professional working environment until you retire you should choose the first option that work on the big and professional company.
If you want to start up your own business you should work in both companies to learn the knowledge and experience from the small company (you can learn much more knowledge, managing skills, adaptability, flexibility in this company) and the professional working method from the big company.
You can combine and design the suitable working environment for your company.
I see a lots of friends who worked for small company then start up successfully while the people worked in the big company can not. Because the start up is rather similar with the small company that you work for.