Omega 3 and Green Tea are good for the skin, have qualities that replenish and make the skin healthier – the first step to clear skin.
I have also been told that keeping the hair super clean and shampoo'ed goes a long way to prevent acne by a dermatologist.Try Murad acne pills. They work amazingly well for me. Also, washing your face with St. Ive's apricot scrub Blemish and Bleakhead control, and applying proactiv afterwards (only the lotion, not the cleanser and toner). And healthy diet (no dairy, sugars, fats).
But to answer your question, I think you need both on regular basis, you can't just do one thing because you have to target acne on all angles. Zinc is used mostly for acne scars though.the thing is if you are zinc deficient it can cause acne. if you need more omega 3's you need the fish oil. there's even a possibility you need both. however… if that is not the root cause of your acne then it will do nothing for you. there are so many possible reasons for a skin problem.

ex. food allergies, a chemical allergy, bad diet, poor digestion, unbalanced hormones

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