Which do you prefer?
I'm 50/50 between them with weighed in pros and cons. I figure I'd share those with you and you can provide your own opinions on which may be better. This mostly applies to PC games, but you might like emulation so I don't see a problem bringing the subject of that along too.
Physical Copies (Pros):
Legitimate Copies - In times where copyright is in a heated debate and trying to find a line in a huge grey area is troublesome. It's much better safe than sorry to have a physical copy on hand than a illegitimate copy floating around that could get you prosecuted.
Bragging Rights - 4 years ago, I felt like a badass when I had a lot of good titles for the NES, SNES and N64 in their physical form. I was proud with the job I had at the time that helped me afford to build this collection, only to lose it several months later. Yeah I was dismayed. But, the one thing physical copies have over digital is that it's much more impressive to showcase the boxart and the completion of a title. Than it is showing just a file explorer window and browsing through a list.
Guaranteed Performance - This is a personal knock on emulation even though I used to be in the scene a decade ago. I'd much, by comparison, prefer a legitimate copy than a digital one. For the reason that the physical copy is guaranteed to work flawlessly without tinkering with settings and banking on certain computer performance that may or may not run said game as much as a console/hand held would.
Resell Value - People would pay a lot more when you're reselling certain copies than they ever would if you're somehow caught selling ROMs or even Repo copies.
Physical Copies (Cons):
Space - Unless you have the room, storing physical copies can be a pain and can make you look like a hoarder if you aren't prepared in advance for the collection you're about to build.
Availability - Finding certain games is abysmal and really plays on a few key factors. Where you're living, what thrift shops are around you, any Goodwills nearby and if there's generosity in local ads that are kind enough to make things affordable for you to get these copies. It'd be nice if some things were produced again, but, progress says otherwise.
Resell Value - This has it's issues and I'm sure you could relate. Finding shady resellers be it in flea markets or the stores I've mentioned above, may make copies priced at an arm and a leg to get them. Even on extremely common titles for their time like Super Mario Bros for the NES, someone will want $12+ for it and that's not really worth it for a common title. Let's throw in condition upkeep while we're at it, people get their panties in a bunch over conditions and I do predict in a couple decades, finding a decent copy of a game will practically be a diamond find no matter what title it is.
Digital Copies (Pros):
Space - It is extremely easy to organize all of your digital titles in however way you want and you don't really have to worry about clutter. Also, they don't take up a lot of space for storage on an HDD, non-PC games that is.
Digital Copies (Cons):
Resell Value - Unless a game is from a digital distributor like Humble Bundle, Bundle Stars.etc and you have keys you can sell under Steam's sale, selling digital games is mostly a miss.
DRM - With physical copies, you don't always have to put up with DRM as often as you run into when it comes to digital copies. With Steam having you to keep it running to run a game can get annoying, granted there is GoG that says "**** that" and allows for DRM-Free alternatives.
Availability - This is mostly in concern regarding to services like Virtual Console, PSN and X-Box Live Arcade. Where, if decided, digital games can be pulled from your account and can be pulled at a whim from being purchased on the digital marketplace. There are still some games that just aren't available in those services that'd be nice to have. Let's not even start with Region Lock...
Those are all the ones I've pulled off the top of my head, I know I could've said more but I want to leave whatever room for what you can come up with.