I have the same problem as the original poster. I rececntly purchased the BF4 Premium Season Pass through the Sony Entertainment Network website and I was only able to download it for the PS4, even though it says on the page that it's playable on both PS3 & PS4 ( otherwise known as 'Cross Buy').
Update: After spending all morning with PSN customer support and EA online support, I came to find out that this "cross-buy" promotion is no longer available. 😕mileysad:
