The big / small company is definitely personal preference. I spent a lot of time working for a large (~2000 employees) fintech giant and there were a lot of good things about it. There was plenty of budget for sending you to conferences and training courses which is really good when you're fairly fresh into the job as you are. However, it was my experience that with a big company exposure to the bigger picture was limited, even exposure to the full solution was limited. I was a
Java Engineer which was cool but my scope of influence was narrow because when working on larger projects you end up developing your own part and then managing job tickets with other teams for database changes, network changes, server resources, configuration management. None of the other teams really care about your project and view your requests with heavy suspicion, especially any team with security featuring high on their set of values.
When I joined my current company there were about 25 of us in the whole company, and probably less than 10 in Engineering. It's a different ballgame altogether but it suits me better. When interviewing for new engineers I like to tell them "You will have the freedom to do what you think is best, and the burden to actually do what you think is best", which really highlights the fact that there are no other teams to do it for you so you'll have to actually do the work yourself. If learning is your thing and thrive on the challenge of rolling your sleeves up to do something you've never done before then a smaller company might be the right fit for you.
Also, as Tim says, you'll have much more visibility to what's going on in the company in general which will help greatly with your understanding of why you're doing what you're doing. You might even have direct contact with the customer, i.e the users of your software, which is less likely in a large company. In fact in the large company I worked for, who operated a financial trading platform, any contact with the customer, the traders, was forbidden because it would likely be viewed by the regulator as insider trading.
I can't tell you which job offer to choose, I can only speak of my own experiences.
Best of luck in your decision.