Well, installing an external hard drive is a lot easier and faster than installing an internal hard drive. If you only plan to use the new hard drive for storage then an external hard drive is ideal. However, if you plan to open and close files frequently on the hard drive then you have to think about speed. An external hard drive can connect to your computer via USB 2.0 or Firewire, their speeds are 480 Mbps and 400 Mbps respectively. This is the bottleneck. Accessing information from a hard drive is significantly faster if it is internal versus external. Another factor is cost. External hard drives are 50% more expensive than internal hard drives.
As for your computer's sluggishness, I believe the problem is with the page file. Oftentimes, Windows converts some of the space on the hard drive to virtual memory in order open and use programs. As a general rule, you should reserve 10% of your hard drive space.