I prefer disc. I like to have my physical collection with me.
- Frees up my HDD (no need to delete for space)
- Don't have to wait to download and install them (speed). I REALLY hate how long this can take, especially for larger games. inFAMOUS 2 took forever!
But they can be damaged and they my require a replacement which will cost some $. With PSN stuff they're forever tied to your account. Plus, if you don't like getting up and changing discs between sessions PSN games are very convenient in this sense.
I also don't like opening my account on my friends' PS3s, but with discs I can just walk with the game (Rayman Origins).
I also prefer discs in situations where the internet is dodgy. I tend to change games frequently, and my HDD is only 120 GB. With patches, games, DLC and updates that's a very small amount of space. So changing games may require me to delete older stuff in order to play the ones I am interested in, which may not be possible when the net is down (in developing countries this is a very real possibility).
If you travel a lot PSN is MUCH more convenient though. My collection is 70+ and growing, so I don't know how I'm going to fit all of that in my suitcase if I decide to return home after I finish my Masters in North America. 
Playstation = The Beast from the East
Sony + Nintendo = WIN! PS3 + PSV + PS4 + Wii U + 3DS
