In terms of overall gaming performance, the Intel Core i7-9800X 8-Core 3.8GHz is massively better than the Intel Core i3-9350KF 4-Core 4.0GHz when it comes to running the latest games. This also means it will be less likely to bottleneck more powerful GPUs, allowing them to achieve more of their gaming performance potential.

The Core i3-9350KF 4-Core was released less than a year after the Core i7-9800X 8-Core, and so they are likely to have similar levels of support, and similarly optimized performance when running the latest games.

Both CPUs exhibit very powerful performance, so it probably isn't worth upgrading from one to the other, as both are capable of running even the most demanding games at the highest settings (assuming they are accompanied by equivalently powerful GPUs).

The Core i7-9800X 8-Core has 4 more cores than the Core i3-9350KF 4-Core. 8 cores is probably excessive if you mean to just run the latest games, as games are not yet able to harness this many cores. The cores in the Core i3-9350KF 4-Core is more than enough for gaming purposes. However, if you intend on running a server with the Core i7-9800X 8-Core, it would seem to be a decent choice.

The Core i7-9800X 8-Core has 12 more threads than the Core i3-9350KF 4-Core. The Core i3-9350KF 4-Core has one thread per physical core, whereas the Core i7-9800X 8-Core uses hyperthreading and has 2 logical threads per physical core.

Multiple threads are useful for improving the performance of multi-threaded applications. Additional cores and their accompanying thread will always be beneficial for multi-threaded applications. Hyperthreading will be beneficial for applications optimized for it, but it may slow others down. For games, the number of threads is largely irrelevant, as long as you have at least 2 cores (preferably 4), and hyperthreading can sometimes even hit performance.

More important for gaming than the number of cores and threads is the clock rate. Problematically, unless the two CPUs are from the same family, this can only serve as a general guide and nothing like an exact comparison, because the clock cycles per instruction (CPI) will vary so much.

The Core i7-9800X 8-Core and Core i3-9350KF 4-Core are not from the same family of CPUs, so their clock speeds are by no means directly comparable. Bear in mind, then, that while the Core i3-9350KF 4-Core has a 0.2 GHz faster frequency, this is not always an indicator that it will be superior in performance, despite frequency being crucial when trying to avoid GPU bottlenecking. As such, we need to look elsewhere for more reliable comparisons.

Aside from the clock rate, the next-most important CPU features for PC game performance are L2 and L3 cache size. Faster than RAM, the more cache available, the more data that can be stored for lightning-fast retrieval. L1 Cache is not usually an issue anymore for gaming, with most high-end CPUs eking out about the same L1 performance, and L2 is more important than L3 - but L3 is still important if you want to reach the highest levels of performance. Bear in mind that although it is better to have a larger cache, the larger it is, the higher the latency, so a balance has to be struck.

The maximum Thermal Design Power is the power in Watts that the CPU will consume in the worst case scenario. The lithography is the semiconductor manufacturing technology being used to create the CPU - the smaller this is, the more transistors that can be fit into the CPU, and the closer the connections. For both the lithography and the TDP, it is the lower the better, because a lower number means a lower amount of power is necessary to run the CPU, and consequently a lower amount of heat is produced.

The Core i3-9350KF 4-Core has a 74 Watt lower Maximum TDP than the Core i7-9800X 8-Core (though they were created with the same size 14 nm manufacturing technology). What this means is the Core i3-9350KF 4-Core will consume significantly less power and consequently produce less heat, enabling more prolonged computational tasks with fewer adverse effects. This will lower your yearly electricity bill significantly, as well as prevent you from having to invest in extra cooling mechanisms (unless you overclock).