I much prefer having physical copies of my games. It's nice to have a big collection of all my favorite games that I can just see. I regret having only a digital copy of New Leaf for multiple reasons, one of which being that if something were to happen to my 3DS one day (which is getting a little old), all my data and catalogued items will be gone.
I prefer to get them physically. I’m only going digital if it’s a third-party game.
There were very few games I got both the digital and physical copy. Super Mario 3D All Stars was one of them due to its limited-time release and my personal history of a house fire.
I mainly buy physical games. I like looking at the cover art, and I like seeing them lined up on my shelves. Also, I buy a lot of visual novels/otome games, and the collector's edition of physical games come with neat things like art books, key chains, posters, etc. The only downside is I'm starting to run out of room!