The rx480 is actually a very good card, now. Early releases had issues with overdrawn wattage on the pcie x16 slot which has since been remedied.
As far as performance goes, its a tie. Depends entirely on the game. Some games are optimized for nvidia cards so the 970 beats the 390 and the 480,some games are more equal where differences between the 480,390x and 980 are a less than 3-4fps either way and some are optimized more for the 480 which tops the 390x and 980 by a decent margin. Generally though, the Rx series has done exactly what the Maxwell cards did. Cut power requirements and consequently the heat involved vrs the prior series cards. The 970 for instance is @3% stronger on most games than a 780ti, so kinda negligible performance upgrade, yet has much lower actual power requirements and heat output. Most games my 970 fans don't even kick on because the card hasn't reached 65°C. The 480 roughly sits right in between the 390 and 390x in performance, so no biggie there either, but that's in a card that's @$100 cheaper than a 390x, has significantly lower actual power requirements and significantly lower heat output. All in all that's a serious step up for amd. All they need now is a 490 to give the Gtx1070 a run for its money. There's a sizable performance difference between a $200 4Gb gtx960 and a $235 8Gb Rx480.