I own hard copies and digital copies.
Digital are nice for travel, as you don't need a whole case to bring your games but hard copies are nice because you can sell them if you want to. Also there's a lot of horror stories of people getting locked out their Nintendo accounts, losing their games or accidentally deleting saves and files.
Story time! I had an instance where I had to replace my DS and the game stop employee didn't let me transfer my files onto my new one. He even tried to convince me that I would get my games back if he simply factory restored my trade-in. Idiot me knew that was wrong but he worked at a gamestop, and I figured he knew what he was talking about.
And I found out you can't even retrieve your Nintendo ID that way. You have to call Nintendo to unlock your account if you don't transfer your files! With that being said, I lost all my saves and had to restart every game from the beginning like new. I was devastated. I still haven't touched a lot of them since. I'm sure digital also risks corruption too. Why else would there be a repair my download button for your copies at the eshop?
But yeah, in my experience physical copies are the only way to go for really nice expensive games. I can deal with losing a save here and there for digital copies so I try not to spend more than $10 on a digital. Because I still think they're great for travel.
- - - Post Merge - - -
I prefer hard copy.
It will never get lost, if you sell your 3DS. Because. You have the physical cartridge.
Don't be like me and forget to transfer your data from one 3DS to another and lose your AC:NL digital copy :"D
However, I might be dumb and get a digital copy, and have my 4th copy of the game, but I'm honestly not sure xD
Did you never try to retrieve your Nintendo id? Because that exact same thing happened to me. You have to call Nintendo America to unlock your account. Then you can download all of your games back, but no saves. It'll be like getting a brand new copy lol.
If you didn't, and just made a new account, this would be a waste of time. But if you ever get another DS, you can keep this in mind and retrieve all your games back.