Intel CPUs use different CPU socket than AMD CPUs do. Your AMD FX series CPU uses AM3+ CPU socket. Intel's Haswell CPUs use LGA1150 CPU socket and Intel's latest Skylake and Kaby Lake CPUs use LGA1151 CPU socket.
If you buy Intel's Haswell CPU then you can reuse your DDR3 RAM since Haswell CPUs also use DDR3 RAM. But if you buy Intel's Skylake or Kaby Lake CPU then you have to buy DDR4 RAM since they use only faster DDR4 RAM.
Few examples.
Haswell build (same components as in my Haswell PC).
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-4590 3.3GHz Quad-Core Processor ($198.99 @ SuperBiiz)
Motherboard: MSI Z97-GAMING 5 ATX LGA1150 Motherboard ($137.37 @ OutletPC)
Total: $336.36
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-01-14 06:47 EST-0500
And Skylake as well (also same components as in my Skylake PC, except CPU).
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($188.99 @ SuperBiiz)
Motherboard: MSI Z170A GAMING M5 ATX LGA1151 Motherboard ($149.88 @ OutletPC)
Memory: Kingston Savage 8GB (2 x 4GB) DDR4-3000 Memory ($74.98 @ Directron)
Total: $413.85
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-01-14 06:50 EST-0500
Currently, both builds perform about the same. Skylake build is slightly faster due to a much faster RAM but both CPUs perform exactly the same.
i5-4590 vs i5-6500:
http://cpu.userbenchmark.com/Compare/Intel-Core-i5-4590-vs-Intel-Core-i5-6500/2604vs3513
With MSI Z97 Gaming 5 MoBo, you can put faster RAM into it and thus remove the advantage of DDR4 RAM. MSI Z97 MoBo supports DDR3 RAM up to speeds of 3300 Mhz.
MSI Z170A Gaming M5 supports DDR4 RAM speeds up to 3600 Mhz.
However, since both builds use Z-series MoBos, you can upgrade both even further and put K-series CPU in them, so you can OC (overclock) the CPU when needed. Best Haswell CPU is i7-4790K, best Skylake CPU is i7-6700K and best Kaby Lake CPU is i7-7700K. You can put Kaby Lake CPU into Z170 chipset MoBo only when you update the BIOS.
As far as those three compare to each other, here's few comparisons as well,
i7-4790K vs i7-6700K:
http://cpu.userbenchmark.com/Compare/Intel-Core-i7-4790K-vs-Intel-Core-i7-6700K/2384vs3502
i7-4790K vs i7-7700K:
http://cpu.userbenchmark.com/Compare/Intel-Core-i7-4790K-vs-Intel-Core-i7-7700K/2384vs3647
i7-6700K vs i7-7700K:
http://cpu.userbenchmark.com/Compare/Intel-Core-i7-6700K-vs-Intel-Core-i7-7700K/3502vs3647
As you can see, there's not much gain between the best Haswell CPU and the best Kaby Lake CPU.
If you're on fairly limited budget then go with Haswell build. But when you have more money and in the future want to upgrade to the Kaby Lake CPU then go with Skylake.