I have a late 2008 MacBook so I know that if I want to connect my laptop to a tv I need two cables: one for video and one for audio (while in newer models this issue is bypassable via appropriate adapters). So using the hdmi port of the mini would make my life easier.
Are there any other advantages?
For example when I first connected my laptop I needed to do some fiddling around with the displays settings to achieve a decent output: would that be necessary with the mini as well?
I've been using laptops for so long I forgot what it's like not having a display already embedded in your computer!