Simply put: In the work you do, size matters.
If you think about it, what you and the hiring manager are doing is seeing if there is a good fit for you on the team - one of the only three things every interview question is about. And scale is a big deal in determining your ability to get the job.
For example, you are interviewing for a position in a company that has 2,000 employees on site in multiple buildings. And you come from a 5-person startup. Do you think either you or the hiring manager are going "not a good fit -- too small/large of a company"? Of course. The agility of a startup against an entrenched, process focused hierarchy. What could go wrong?
If you are a manager of six people, do you think the hiring manager would believe that your six people don't match up with the 4-directs and 24 other people reporting to those directs? Probably not. The scale of your current job isn't big enough.
There is a lot about scale to have in your resume, sprinkled in with your accomplishments. Here are four ways to look at scale:
The more dollars you are responsible for, the bigger the job. Whether that is a departmental budget, project budget, or some portion of a budget, the size of the budget matters.
This could be direct supervision, the number of directs who report to you and the number of people that report to your directs, to the number of people involved in a project. People are always an important measurement of scale.
Projects are unique entities, but have very good statistics when it comes to scale. Project budget, number of people managed, of course. The number of hours associated with the project is another good metric -- maybe you only had six people on the project, but it took 10,000 hours to complete the project. It's a big one.
This could be the number of people working for your current manager, something larger around, say, a director's group, or something in-between. Just pick something that makes it easily explainable in an interview.
The key here is not that a global company with 50,000 people working in it is better than a 50-person local company. The key is trying to fit into a new environment. You know without me telling you that a global employee with 50,000 employees is going to be given a long, hard look by someone hiring for a 50-person company. And you already know all the reasons.
The key is not size, but trying to find the right fit for the right reasons. Size matters, but the fit matters more.