The items only work on te system they were purchased for.
The expansion pass will be fine on both systems.
See destiny's upgrade site for more detail:
http://www.destinythegame.com/digital-upgrade
English
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Since the link provided refers to digital purchases, I feel I need ask if the part about the Expansion Pass still applies when I purchased - both for PS3 & PS4 - physical copies of Destiny.
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The expansion pass is not limited to digital content in the link. It simply refers to the expansion pass. The digital limitation is applied to the base game only.