All though many argue total white hat not to interlink if you do redirect SITE A to site B you will find a bit of a hit on site B's authority. I've seen it done a few times and work well especially if the content it the same/similar. 301 is telling Google "this is the permanent new home of this page".
If you're planning on shutting down Site A and Site B is similar content I don't see why a 301 wouldn't work.
301 and links technically work about the same on passing link juice its more a case of what work better for the situation.
As touched on by Gary whilst this is great it can also have longer term problems though that's not a guarantee that your page will rank. It depends if you want to stay completely white hat or more a bit more grey though if you ask me there is no white hat only shades of grey..
As I always recommend lots of research and advice never hurt and once you've got it all you can then work on an informed choice.
Good luck.