You can do work across such a connection, but it can be, well, sticky. You get typing fast enough, and you will find yourself sentences ahead of what's appearing on the screen. It will catch up, but it can be frustrating. Basically, anything you can do on your computer at work, you can do at home. The key difference between remote control and remote access is that in the former, the translation between the office computer and your home PC introduces a delay.
Directory services are another key feature of remote-control programs.
You can copy individual files or whole directories from work to home and vice versa. This can be quite useful for people who keep directories and to-do lists on their computers, because with a little thought, the important stuff on your home system can be mirrored to your office, and your office stuff to home. This isn't just a matter of convenience, it is also a useful backup and disaster-recovery system. Think about it. You have to call the office drive something, and you can't call it drive C because that letter is already taken on your home computer.