The hyperlinks to the builds did not paste correctly.
If you are going to multi-task with the PC, I'd go with 8 cores because they will definitely help if you do video re-encoding (e.g. backing up your Blu-ray collection), although 6 cores are a sweet spot. Since you are a Linux user, bear in mind the GPU drivers between AMD and Nvidia. Last time I checked, the Nvidia drivers are not well liked among the Linux community.
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@Monsieur Xavier said, when it comes to GPUs Nvidia is king. If you want performance/price ratio, then AMD is the way especially for the CPU. Another thing to consider, Intel's CPUs with K suffix do not offer a cooler. The 3700X and 3800X both include a decent cooler so you can still buy an aftermarket one months later. Also, they are both 7nm so they are smaller than Intel's (14nm) so less heat/more energy efficient if you care about that.
Between the 3700X and 3800X, the former is the better deal:
UserBenchmark: AMD Ryzen 7 3700X vs 3800X
11600K vs 10700K, the former is better (also more recent):
UserBenchmark: Intel Core i5-11600K vs i7-10700K
The 11600K is apparently the winner against the 3700X:
UserBenchmark: AMD Ryzen 7 3700X vs Intel Core i5-11600K