The i5-10400/10400F is also a decent option, but it does not really beat the 3600 in gaming, and the 3600 tends to be slightly ahead in terms of application performance. While the higher-end, unlocked 10-series chips tend to hold a small performance edge over the Ryzen 3000 series in CPU-limited games, the lower clocks of the 10400 only allow it to perform roughly on-par with the 3600. If it is paired with similar RAM and a Z-series motherboard to enable those faster RAM speeds (since Intel arbitrarily locks non-overclocking boards out of running RAM at speeds higher than DDR4-2666), it can potentially perform slightly faster in some titles provided those criteria are met, but we are talking about margin-of-error differences, and that's generally only when paired with a very high-end graphics card running at low resolutions. If the 10400 is paired with a board that can't run RAM at more than 2666 speed, then the Ryzen 3600 is often shown to perform slightly faster in games.
Again though, we are talking about margin-of-error differences, and in terms of realistic setups, the graphics card is likely to be the limiting factor for gaming performance in nearly all scenarios, making a Ryzen 3600 and an i5-10400 nearly identical in terms of gaming performance. The 10400 does hold a small price advantage currently, though a Z-series motherboard with comparable features will tend to cost a bit more than AMD's offerings, countering much of that. It is an option worth considering though.