The 7870 is better than the 7850, but it's not an earthshattering difference. The ZS 550W is also sufficient for the 7870 and overclocking. Another PSU recommendation is the XFX Core 550W: http://www.amazon.co.uk/XFX-P1-550S-XXB9-PRO550W-Edition-Supply/dp/B004RJ8EKI/ref=sr_1_2?ie=UTF8&qid=1342029957&sr=8-2
It has 6A more on the 12V rails, two more years of warranty, costs the same, and is made by Seasonic - arguably the best PSU mfr on the street. Between those two I would definitely go for the XFX Core 550W.