I personally prefer physical copies. I really like opening new games, especially ones I've been waiting a very long time for.
Digital copies are cool, and definitely very convenient, but I like to actually have the packaging in front of me. I also like having game boxes on display, so I can easily find my games without having to turn a system on and use the menu. It's also a way for my friends to see what games I have without me having to show them right on my 3DS.
I can honestly say that I am considering a switch over to digital copies, simply because eventually they might be cheaper and released earlier.