General purpose cpu as logic analyser better / worse than dedicated FPGA implementation
Your typical 3GHz x86 CPU is going to require so much stuff around it to get it going that once you got started you would begin to wonder just what the dickens you were thinking about. 

The modern x86 CPU has no GPIOs as we think of it. Instead is has special ports for DDR4 or DDR4 memory DIMS, PCIe ports to hook to other controller boards or chips, and something called a DMI link to connect to a motherboard chipset component called a PCH. The PCH will have to have a SPI flash connected to provide the BIOS to boot up such CPU. And do not forget all the voltage regulators needed to power up a modern CPU and chipset and DDR memory. You could expect to have as many as 12 or 15 voltage regulators to get it all going. 

Forget your x86 CPU idea and use the FPGA. You can outfit an FPGA on a board with way fewer components. The FPGA also allows for the wide and complex sequential triggers that are needed for a decent logic analyzer implementation working in parallel with sampling. Not something you can ever do with an x86 CPU running a linear program thread.