Personally, I don't use either, but I think digital downloads are going to overtake Blu-Ray. They're faster, more convenient, cheaper (you don't have to buy a $600 player), and you can probably get close to the same quality. For a Blu-Ray disc, you have to go to the store, find the player and movies, wait in line to buy them, drive home, hook up the player, and then you can play the movie. Probably two hours total, depending on how efficient your store is and how complicated your home theater system is. For digital downloads, you download them from a website and play them on your computer. Probably a half hour, depending on how fast your Internet connection is.
Plus, you have more variety in your selection. You can probably find tens of thousands, maybe hundreds of thousands, of movies online. At your local video store, you can probably find a few thousand.
I'll cast my bet with digital downloads. 2020 at the latest and Blu-Ray will be as out-of-date as the VCR.