So I have two big named companies who have offered me a job after I graduate from college... Choice A is a defense contracting and technology company in the US and is very reputable. While, Choice B is a higher education software company and is reputable but not as popular as choice A.

I enjoy both work and think both would be a great platform for my career, however I don't know how heavy the weight of choice A's (more reputable) name on my resume will carry when applying for mid-career level jobs than Choice B.

Should I even worry about the name of the company?... Or mainly worry about what I would be doing at each company?