I once had a professor at university who asked us students what kind of company we would try to get into once we had finished our studies. A few of us mentioned the names of very large companies. Our professor then said to us that we should start with smaller companies or even start our own. Once we were 50 we could still join the large companies to prepare for retirement...
That's what the professor said. Partially I agree with this. If you are looking for a role in which you can make a difference without being limited by a gazillion policies, processes and rules then maybe a smaller company might be the better choice. But then there are also large companies which have departments that function very much like a start-up.
Ask questions to find out about the culture in the particular team. Then try to assess whether this is the kind of team you are looking for. Forget about the size of the company. A large company does not offer more job security than small ones, see Kodak, Nokia, etc. I would recommend to find out whether you are a good fit for the team and whether the team is a good fit for you.