You can look at TomsHardware, TechSpot, Guru3D.
3600 beats the 2600X in TomsHardware's guide by about 10-15% across the board.
Techspot compares 3600 to 2600 and there are substantial gains between the two - 3600 scores 102 points more on CB20 single-core and ~800 more points multicore (gains of >25%). Other productivity benchmarks are 10-20% gains. Gaming is about 15-20% gain, sometimes even more, at 1080p. It also uses less power to win by that much.
Guru3D got similar results.
Overall, with the 2600 at $117 and the 3600 at $189, the gains might not be worth it for you.
You could also consider getting a 2700X for $159 (best price I could find) which at 8C/16T wins in productivity, but it's ~5% slower in gaming than the 3600. But for saving almost 20% in cost, may be worth it. Also, it consumes a LOT more power, like 30-40% more power at load than the 3600.
In the end that's not an easy answer to give. I could tell you I have a 3600 and it's a great chip. But I couldn't tell you how much better than a 2600 or 2700X it is, personally, without referencing reviews.