I've done both.
The first six years of my career was for a software company where I was on a team which did desktop support, server operations, backups, network architecture -- you name it, we did it. All that and the configuration management/release management for the product too. Through that six years I was twice offered the open door into entry-level management.
Since then I've been an employee at a company which provides contract services to customers of varying sizes (think being a consultant without having to find my own customers). I've had both long-term customers (like eight of the nine years I've been here) and one-visit, hit-and-run jobs. I've done everything from being a one-man IT department to being highly focused on one small part of a massive project.
There are advantages and disadvantages to both.
Currently I enjoy being the go-to guy for my long-term customers (even though coincidentally both are ending shortly for unrelated reasons). I have built fairly robust networks at both pieces and I have the architecture, and reasons for that architecture, in my head. Even though one site is fairly well documented, it is kind of neat to me to be able to tell people the reasoning behind the choices made.
Of course the goal is to document everything, and that philosophy is what drives answers like this: If you got hit by a bus, would your company be in trouble?
There is also the constant change of scenery and moving around to visit different sites at different times. Plus the occasional rush when something blows up somewhere and you have to rush to be the hero of the hour. (Or try, anyways).
There are downsides. Some of our customers go against our recommendations, resulting in the very fires we have to rush to fix. Sometimes it is tiring to be on the road all the time. Sometimes it is worrying when there isn't enough to do and you start to wonder how your employer will pay you.
My big negative right now is that it is hard to take comp time when overtime or special jobs happen. The problem is that even if you work an extra 8 hours for customer A, you can't take the comp time the next day because those are scheduled visits to customers B C and D, none of which had anything to do with the overtime happened.
And a long-term negative, one which surprised me, is that I miss having a regular, daily commute and a cubical to hang all the artwork the kids do in school in.
I periodically look at the help-wanted and jobs boards to see what is available, but I have not hit that magic combination where the job was interesting and I was at a negative enough point in my cycle with my current job to want to apply.
Eventually I'll probably switch back if I find an interesting enough job.