Do you think working for a well known company makes you more valuable?

When I was in college I dreamed of graduating and getting a job offer from a major company like Google, Facebook, Microsoft, Twitter, etc. I assumed it would be an emblem of my knowledge and skills. I also assumed having a big name like that on my resume would mean I'd automatically get a foot in the door at any company in the world, in the slight change I chose to change jobs.

That dream didn't pan out and I never heard back from any of those big companies I applied to. Absurd, I know! Since then I've only worked for no-name boring companies doing mediocre software engineering tasks getting no where in life. Kidding!

Like many of you working at no-name companies, I love my job! Seriously, I feel like the experience I'm gaining is far superior to what I'd get working for one of those major companies. I wear many hats such as: DBA, server admin, and full-stack developer. I am continually learning and my job challenges me daily. Not to mention I work from home ;) I love my job so much I feel like it's more valuable than a job any of those big companies could offer me. I don't care to work for them anymore and I believe those jobs are hyped up. Don't get me wrong, I believe they offer great experiences too, just not more than anywhere else.

So I'd like to hear some thoughts on this topic. Is working for a major company better in the long run? Does it give people an unfair advantage, or does it limit them?

Will they get more experience working there compared to a startup?

I understand every job is different and there's no simple answer to these questions. However, these thoughts have been on my mind for a while and I'd like to have a discussion about it.

Cheers!