The 7770 is substantially better for gaming but Skylake has full hardware decode support for modern codecs (e.g. HEVC) and of course the 7770 is going to have much higher TDP and extra fan noise. The answer to that question for the most part comes down to whether or not you card about fill rates and extra texture memory for any reason.
The 7770 is a respectable, contemporary card for 720p gaming with GDDR5, 72GB/s of memory bandwidth and a fill rate of 16GPixels/s on a TDP of 80W. The HD530 graphics in the Skylake i3 are based on DDR3/4, 12GB/s or 17GB/s memory transfer rate (depending on your RAM), 1 or 3GPixels fill rate and a "free since it's in the CPU you're already using" TDP of 55W. Skylake is pathetic in terms of horsepower, but it's entirely probable that you don't care.
The best concentrated resource I know of for Apples to Oranges hardware comparisons is the
TechARP GPU List.