Does company name or the experience matter more in internships

I’m studying CS and I’ve got an offer from a Big 4 firm for a data science internship. At the same time, my friend is referring me to a mid-sized company where he had a really good experience and got to run his own mini project.

I’ve done more software engineering stuff so far, and honestly I didn’t really enjoy the data science module I took. Because of that, I’m leaning more towards the mid-sized company since it feels more aligned with what I actually like and want to do.

The only thing making me hesitate is the Big 4 name. I know it stands out on a CV, and I sometimes wonder whether recruiters might care more about the brand than the actual work you did.