Hey @jcmcneal ! For what it's worth, i've been working for a kind of big french company the past two years. I've learned a lot and I met really nice and competent people. All was pretty good at the beginning though, and it started to change when managers dediced to assign me to another team, for another task.... Things became to be boring and for 10 months I had not saw a line of code. So I left this job to work in an IT Services company. It's been 5 months now and I already have responsabilites, I can finally develop software and I'm learning form even talented person. To answser your questions, I think you'll get more experienced whereever you go with a bit of luck, could it be Google or the startup in your garage. I think it's better in long run espacially for big companies though because it demonstate that they keep up with you and if you're not working there anymore it's because you wanted it (don't know if i'm clear :$). To conclude, yes I think working for big companies is a door opener and gives you an advantage in an interview.
Hope I answered your questions. Have a good one, cheers !