In the start of my career, I worked for startup companies. I don't know but during those days, when I tried to apply for any mid-level or MNC for job opportunities, I never received call from them or let just say HR rejected the applications because my resume had startup companies mentioned in my resume. For few I did get calls, but I came to know from someone (via some source) that those companies mostly prefer people having work experience in MNc's (big companies) and they are very reluctant to hire people having work experience from small comapnies. And same is true for good funded startups.
Currently, I'm working in a big investment banking company as Software Engineer. I have offer from few startups (5-10 years old) and some staffing companies to be deployed on their client location. Would my future job opprotunities suffer again if I move from big to small?