What is your favorite way of mining between the two? Mine has to be branch mining at level 10, it's clean, organized and you have a higher chance of finding ores.
I like branch mining just because I don't mind all the extra cobble. Makes it easier to start larger building projects.
That's one good reason to like strip mining, but in my case I don't need cobblestone for the time being. I have 4 double chests full of it.