hyper threaded core i3 vs non-hyper threaded core i5

I have been searching around and comparing specifications to build a budget gaming PC. On the Intel site, i have been comparing CPUs and I noticed that the I3 CPUs, while only having 2 physical cores as usual, have 4 threads, meaning that they are hyper threaded. But with the I5 CPUs on the other hand, they have 4 physical cores and 4 threads, meaning that they are not hyper threaded, which is kinda weird for intel to hyper thread the I3s and I7s but not the I5s. As common knowledge, virtual cores (made by hyper threading) are of course, less powerful than physical cores. but the I3 CPUs also have significantly more clock speed, with the I3 CPUS varying between 3.3 and 3.9 GHz, and the I5 CPUs between 2.7 and 3.3 GHz (discounting K CPUs).

I would like to which CPU is faster (in gaming and everyday computing performance): the I3-6100 or the I5-6500 at double the price. While pricing may suggest that I5-6500 is more powerful (you get what you pay for), the specifications shows that the I3-6100 has the same number of threads but significantly higher clock speed (overwhelming the inefficiency caused by virtual cores), suggesting that it is more powerful (the I3-6100 has 4 MB of cache while the I5-6500 has 6 MB of cache, but cache sizes doesn't affect performance very much, do they?). Or is there something wrong in my logic? And if there is indeed an error with my logic, could someone please correct it?

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