This is my personal opinion and please take it with several grains of salt considering I only graduated last May. I've always heard it said that it's harder to move from small to large than large to small, however, I work at a small public firm and I find the experience is 1000000x better than any of the bigger companies I interned at. If you feel like you're being pigeonholed into one aspect of accounting at a small company I might be concerned.
At my small firm (about 15 people) I get to do bookkeeping, audits (with plenty of supervision), payroll tax, sales tax in various states, business tax, financial reporting (including the IT side of our program and construction the statements), and many other various projects for the firm or for clients.. The only thing I really don't get to do is individual tax which I am more than ok with!
I've personally seen this as the big advantage a small firm has over the larger firms. At large firms you get mediocre experience to start off (since you generally do just 1 thing) but a great reputation to go somewhere. At small firms you get great experience because of the small number of people you'll have to have your hand in almost everything, but the reputation is mediocre since one knows or cares about joe shmoes accounting firm.
I'd say if you're at a small firm and feel like you aren't getting good experience in a lot of areas or don't have the potential to anytime soon, maybe I'd look around for something else. Keep in mind I just graduated and have only been at this firm for less than 1 year…
Hopefully that helps!