I'm envious of the experience some people get at smaller places. They have to know a LOT more and have a wider knowledge base. It's really worth doing something like that for a couple of years, the experience you get would be very valuable.
When you work at a larger place it's much more specialsed. The network team don't have time to be worrying about looking after servers as well.
I am with you
I work with ~20 servers and 125 users over 5 sites and I am the only IT person here
I am very busy as you can imagine and we do pretty much everything in house, very rarely have consultants or engineers in, so I have a vast range of experience, from installing new servers, racks, networks, storage. Unix & windows systems, email, IIS, SQL etc etc. I love the variety, which is, looking at the job pages, very rare indeed. Every job I have looked at in the past 6 months is for a specific area, like Network Admin, Database admin. There are very few jobs like mine about, which is going to make it hard to move on