I open mostly. Toy quality and play value has always been really important to me as a collector. The only way to judge that is to open them up... to feel and smell the plastic. But I love the packaging also. If I could afford it, and if I had the room to store or even display everything, I'd do both. As is, I'll only keep a double of the ones that I like the most carded or boxed. Also trying to keep at least one of every card or box style in my collection.
I'm a total pack-rat when it comes to the card backs and stuff also. I'll open a figure then toss the paper stuff in a drawer for future "reference." Sometime years later I'll go through this one filing cabinet drawer and throw everything away... but it's so hard to do.