Between the two I prefer miiverse, but miiverse takes forever to load, so I rarely ever upload any screenshots. I take pictures of pretty much everything I do. Haha. They're in my album, but I'd rather not remove my SD and upload anything.
I used the L&R buttons for a long time until I learned about the Miiverse method last month during the Christmas screenshot contest. I haven't taken a screenshot since that time though, so I don't really have a preference at the moment.
In theory, I like the idea of the L&R button screenshots better because I don't have any interest in using Miiverse and don't want to inundate friends on the Wii U with random screenshots. That said, I currently lack an SD card reader that has a slot the correct size for the 3DS SD card, so Miiverse would be more convenient until I buy one.