I've worked for companies from 200-350,000 employee's. There are pro's and con's to working at both large and small companies.
Unfortunately bad management isn't exclusive to large companies as I've seen bad management at both. Larger companies tend to have more polices thanks to stupid regulations such as SOX. Chances are if they are large they are public.
Internal movement both lateral and vertical can be difficult with small companies. With larger companies there are plenty of opportunities in house which means you can move around without leaving the company. I have also found its easy to branch into new roles. If you have proven yourself then they know you'll ramp quickly and be able to produce. I always liked that. However, with smaller companies you have a better chance of becoming involved in making decisions that affect the company.
I'm at a small company now and its nice to have more control, not as much red tape because we aren't public, exposure to different technologies. With large companies you tend to be silo'd to your specific skillset. What I don't like is that the systems I manage are not as complex as they were in large companies. I enjoy working with highly available, critical environments where downtime can cost the company millions. On the other hand the job isn't as stressful and there's more family time.
With the type of work I do, in larger companies your usually in a group of similar people. The nice thing about this is that there are people to bounce ideas off, different sets of eyes when looking at a problem, others with more experience in certain areas. All this can provide you with more opportunities to learn.
Anyways, i'm sure we could go on for quite awhile generalizing about the pros/cons of working in both large and small companies. Personally I wouldn't rule out working for either. As long as the job is stimulating and provides me with opportunities to learn then i'll be happy. I tend to move on if things become stagnant.