Well, I've been in both the big corporation (I don't recall the number of employee's we supported but it was the entire Western Hemisphere and the projects were global) and the "One man show".
It's tough...
In the big corporation Wiilir is correct, if you're not a complete politician, advancing can become more than challenging. Everytime I took two steps forward, I suddenly spent more and more time defending why I took those two steps instead of just moving forward. In addition, the bigger the company the harder it is to advance. Whether or not you've proven yourself your supervisor has to sell others on your abilities and that you deserve to advance.
The pro's? You get to see A LOT more of the current technology than you do in a smaller shop. You'll have a greater access to resouces (namely other people who know more than you do), which can greatly increase how comfortable you are with newer technology.
In a small shop, there's almost no politics. The only type of politicing I currently do is to get the facility to front the cash for improvements to the current technology that we have. I'm in charge of all projects, it has allowed me to get my hands on technology that I couldn't in a larger environment (doing an AD rollout for example).
Con's? You have no safety net. There isn't anyone else to catch if you make a mistake or to help you make deadlines. There aren't many people who will understand what you do, therefore getting support for projects can be a problem (unless you have people around you that you've earned their trust).
Obviously there are greater differences than I've listed here. Personally, I do miss the variety of people from the larger environment and being able to spend money like there's no tomorrow. However, the freedom of the smaller environment is extremely appealing, at least for me. I find the upgrades that I feel are necessary and create the proposal's, learn the technology, and do the implimentation.