You have to realize that "large" and "small" are relative terms. The company I spent my first 7 years in the field with had a maximum of 13 guys total (including apprentices) and averaged about 7. When I went to work for a company that had ~50 guys I thought that was enormous.
You may get a lot of different opinions on this but the truth is that only you know the answer. It all depends on what you want out of the company that you work for. Obviously there will be more opportunity for advancement in a larger company, but you will be moving to a larger pond where more aggresive fish may lurk. In my experience jumping for money is generally not satisfying, and when you do it once it is the beginning of a pattern. At some point you will be looking for a job and the employer is going to have second thoughts about investing in an employee that has 8 different companies he has worked for in the past 10 years.
That doesn't mean I don't think you shouldn't seek the best position for yourself, just that there are other measures of a good employer besides $/hr. If you really don't enjoy where you are, and can make an informed decision about another company (and the larger ones are fairly easy to find out about) and you think it is a good match, than take a chance. If on the other hand you're just thinking that the grass must be greener somewhere else I would caution you.
As I said it depends on what you are looking for. When I worked for the company I mentioned earlier I knew that the entire time I worked for them I could have made more money somewhere else but the whole dynamic was worth it to me to sacrifice some money. I was pretty much left alone, and the two owners were good guys to work for. If I hadn't moved I probably would still be working for them. I recently went back to visit that area of the world and made it a point to have lunch with them.
Again, it all depends on what you are looking for.