I'm currently a SysAdmin working on becoming a Network Engineer.
Being a SysAdmin is cool. I have full admin rights to every computer at my company (except for the AS/400's, those guys hold REAL power). However, I am learning to become a Network Engineer. I'm learning Cisco Switches and Routers, Frame Relay. CSU's & DSU's, etc. I've set up a couple of small (less than 25 users) sites at my company already, and I was allowed to set up one of our newer Internet T-1's by myself. It's a blast! I'm not great at it, but I'm learning!
I think I was more cut out for hardware than software!