I don't think the big company/small company divide is as big as people pretend it is. 90% of whether something is a good job depends on the people you have to rely on and interact with. You'll have small companies where the owner is a dictator, and large companies where your manager and other team members are wonderful to work with and help you grow. You'll also have the exact opposite thing.
In a big company, an office in one city is likely run completely differently than an office in a different city, depending on who's in charge locally. The money all ends up in one place, but an engineering office can only be standardized to a certain extent.
The problem is, identifying the good small company, or good large company office only really happens by getting inside information from people you know. So, starting out, just try for things that look good. You could end up in the small five person office with the owner that cares, or a large company that has a formalized training system. That'd be great. You could also end up in the chaotic small office with no checking procedures, bottom of the barrel copy and paste engineering and no teaching skills, or the big company that has you design anchor bolts with a spreadsheet for four years.
Try to get a feel for the people when you interview, but don't be afraid to leave a job that isn't helping you grow. To a certain extent, the only way to figure out what's a good fit is to try.