In some cases, the difference is quite noticeable. Most external drives aren't chosen for speed, but for reliability, low power requirements, and lower cost. So, while you can probably get the same drives (inside the external cases) and install them internally, I'd recommend going for faster drives overall. My experience so far with my Toshiba X series drive is it's a fast HDD.
Also, if you're installing games on an external drive, any PC you plan on playing it on will require an install, plus the inconvenience of it not being there when the drive isn't plugged in... The inconvenience is there also if you just use the external drive for game saves. (Not all games will let you say where you want to save game saves, not even in their...