GPU has more hash rate in mining a Radeon RX 480, the 4GB or 8GB?

In general, 4GB is sufficient for even the most demanding hashing algorithms and you will not see any performance gains just by having more memory. This is where the speed and quality of the memory comes into play. The 8GB RX 480 has a higher memory clock speed which gives it a slight edge while running memory intensive algorithms such as Ethash (used by Ethereum). When running at the same core clock, the hashing speed of a 8GB RX 480 can be higher by 25–30 hash/sec compared to the 4GB RX 480.

However, hashing speed also depends on the quality of the GDDR5 memory. Samsung based chips seem to perform little better (20–25 hash/sec) compared to Hynix or Elpida. They are also easier to overclock. If the price difference is less than 50 US dollars/euros, I would recommend going for the 8GB version. In case GPU mining becomes less profitable, you can always use the 8GB card for gaming or sell it to someone interested in doing so.