According to Techspot i5 8400 is notably faster than the Ryzen 1600 even when it is heavily overclocked in 720p, slightly faster in 1080p and all this data includes the outlier that is Civ 6. If you don't play that one game the gap is even wider in favour of the 8400.
There isn't a huge amount in it but you basically are forced into heavily overclocking the 1600 to 4GHz which isn't always possible (my friend's sample only does 3.8GHz) to get mostly inferior gaming performance to the 8400 right out of the box. You pays your money and takes your choice. 8400 can be harder to get hold of right now and the boards are more expensive, but it'll only last another couple months.
Considering other outlet data on the 8400 (e.g PC Gamer) I have seen and comparisons with various cards the 8400 holds strong and is faster in most scenarios, often significantly so.
"Measurably", I'll give...but I'm not sure that "noticeably" qualifies when their average was just under
8% at 720p (153 vs. 142), & only
1.5% at 1080p (132 vs. 130)... or that at 1440p (albeit a resolution where the GPU starts holding your system back) the i5 technically
lost to the OC'd Ryzen CPU (107 vs. 108, or a -1% drop).
Of course, I suppose we should throw out the Civilization VI results, since they actually showed the R5 1600 outperforming the i5-8400 (even without an OC), since that's not "fair"...