The main concern I'm having is that I played the Beta during the free weekend and went to the moon, so I know I'm eligible for the emblem. However, I did this on the Xbox 360 and I am now working my way to preordering the PS4 Destiny bundle. I understand that so far that getting the emblem has something to do with linking accounts and so far, I've linked my Xbox account and my PSN account (The same one from PS3, which I'm sure can go to PS4). Will I still be getting the Beta emblem?
The only account that you will have your beta emblem on is the one you participated in the beta with. Since you played on Xbox 360, you can use your beta rewards on Xbox 360 and/or Xbox One (as long as you're on the same XBL account).
I'm not 100% sure, but it is safe to assume that the emblem is tied to the account that you played on and if your b.net account has both your XBL and PSN accounts linked to it you should be able to transfer it. Don't quote me on it, just seems logical.