So, I played battlefield 4 after getting premium and all the DLC and when I signed in and played it on the Xbox One. It did not ask me to transfer stats and when I log into battlelog, it says I have ...
You may want to download Premium again from the purchase history on the Xbox 360. Please also keep in mind that you must have purchased Premium directly on the account itself, and not on an alternate account on your console.
If you purchased Premium on that account and console, then you may want to contact an Electronic Arts Technical Support adviser here to get Premium properly functioning on your Xbox 360.
Steps to contact Support are listed in this spoiler:
1) Click on the game you're having trouble with. (If you don't see it, use the search bar)
2) Select the platform you're playing on/are having problems with.
3) Select a topic and list a short description of your problem.
4) Select the way in which you would like to contact EA. (Options may vary depending on the problem you're having, and your location.)
Remember to be kind, respectful, and patient with your Support Adviser. Your problem may not be resolved right then and there, but they will do their best to get it resolved as quickly as possible. Thank you!
I agree with Apollo, redownload on your 360 and then play a round on 360 to see if Battlelog syncs up. Since you're on your computer it's easiest to log into the Xbox Live site at http://www.xbox.com/en-US/ and then go to "My Account" and then "Download History" and then scroll down until you see your Premium file and click "Add to Queue" and then the next time you log into your Xbox your queued items will automatically download to your Xbox