I think there is something to the physicality of the DVDs that has value to you. So you should keep them. Plus, if you go digital, it will cost a lot of money. Unless there is a pressing need for the space these DVDs take up, I see no need to spend all that money. But the reality is that a "collection" of digital movies is not really a collection. You don't get the artwork of the covers. You can't gaze at your whole collection at once and take satisfaction at the size of it. And that is probably important to you. If it isn't, then maybe you could go digital and not lose something. But I'm guessing the physicality of a DVD is just as important as the actual movie to you. There is absolutely no reason to feel guilty if it is. That kind of thing is the whole point of collecting anything. If that kind of pleasure didn't exist, why collect anything?
But here's the real reason why you should keep them: because you're a MAN, not a wimpy beta who needs to justify himself to his girlfriend. If you want them, keep them, and that's the only reason you need to tell your girlfriend. Trust me on this, women do not like men who cave on shit like this. You'll get more respect from your girlfriend if you simply say something like this: "I've thought it over and I'm keeping them. I like the physicality and artwork of the cases." Don't say more than that. If you're having problems at this point, it means you have to improve your relationship game. See:
http://www.reddit.com/r/TheRedPill/ Be an alpha and your girlfriend will fuck you like you deserve.
Now I am going to give my thoughts on books, because my opinion is different on them.
I have switched to reading nearly all of my books digitally. I really don't like reading a physical book anymore. It's all because of highlighting and notes. I read mostly non-fiction books and in the past when I was only reading physical books, I would try to take notes while I read the important books. I rarely did this though. Now, reading on an iPad, it's really easy to take notes right in the kindle or scribd app. Kindle also allows you to highlight in 4 colors. This has been huge for me. I have a system where I highlight sources red, facts and other data blue, quotes from outside authors orange, and everything else yellow.
The other thing that is great about ebooks is that you can get definition and a wiki entry just by pressing on the word. Breaking out a dictionary is a pain in the ass, and when I read physical books I would only do so when I couldn't get an idea of what the word meant via context clues. Well, it turns out I am terrible at figuring out word meanings via context clues. I've found that certain words have a totally different meaning than I once thought. So in the past, I was misunderstanding tons of shit. This is a major problem when you read old books. A lot of dead words are used in old books.
The other issue is space. I have several hundred books on my iPad. I'd need another room in my house to store all those books. A lot of those books I haven't read. Really old books are usually free in the kindle store because their copyright has expired. So I have a library of probably 200 classic books that I got for free. I didn't have to pay for them and I don't have to store them. Good deal.