I've had a pretty diverse career so far I think.
Back in the day, one of my first jobs was for an International Bank - in my building there were 1000+ employees - I was in customer service (internet banking) and so our floor was roughly 200 people.
Jobs like this, your just a number. Turn over rates can be high and you might be needed but at the end of the day; if you left, you can be replaced. Working for big companies IMO shows you can work with or deal with at least, a big team and tons of opinions but in this case, we had incoming phone calls and so long as the phone and emails were answered - business as usual.
I worked for a big local company (> 500 employees) - here I was in IT (1 of 2 sys admins) - my opinion mattered much more - we were responsible for everything and anything IT related from server deploys to choosing and pricing equipment to help desk type tasks to opening remote offices. This job has looked most impressive on my resume to new employers and for sure, I got most of my experience at this job. Again - did working for a big company help? Kinda - it showed I could work on a team; being such a small IT team, work in many difference scenarios and different projects - but I'm not sure the size got me the jobs that followed; it was my experience they were looking for.
My current job is a local company around 15 employees now - I got this job based on side work experience more then anything else. They liked that I had experience hosting on Rackspace (side job experience), could handle server side and programming side tasks (experience from local > 500 employee company) and could answer support emails when need (bank experience back in the day). None of these companies were or are the Google or FB of the world so did it matter the size or reach of the company? I don't think so... my experience has always gotten me in the door more then big names on my resume.
(aside) ... I much prefer to work for small local companies. I love my boss and it's a very family feeling office. We're casual with each other and theres no corporate politic crap to deal with. so long as the work gets done, we can do as we please, often going to lunch for an hour, having a drink, chatting about movies and politics, etc...
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