Definitely avoid the FX-9590. It's pre-OCd, which means it's going to suck a lot of power & generate a lot of heat, pretty much guaranteeing the need for an aftermarket cooler from the start.
The i5 will perform better than the FX-8350. However, as @Obakasama pointed out, it's as limited as the AMD chip, because its socket is no longer supported (Skylake & future chips are going to use the Socket 1151 platform, while the i5-4690K uses the incompatible Socket 1150), plus it also is limited to DDR3 RAM.
There are some other questions that need to be answered first, though:
1) Do you plan to OC your system? This isn't important if you go with an AMD build, as AMD caters to the enthusiast crowd by keeping all of their chips (FX series, APUs, etc.) "unlocked" so that they can be OC'd (technically even the FX-9590 is still "unlocked", it's just pre-OC'd so much that you can't push it too much farther). Intel, OTOH, sells their chips in "locked" & "unlocked" flavors. The "locked" chips can't be OC'd (or at least not very far, & apparently only with certain motherboards... & I keep seeing that Intel tries to keep up by releasing driver/BIOS updates that blocks it again anyway), but sell for a lot cheaper than the "unlocked" 'K' chips. Also, while not necessarily a big expense, the unlocked "K" chips from Intel aren't sold with a stock cooler, forcing you to buy an aftermarket cooler even if you don't end up OC'ing the chip, which further increases the base cost for the Intel chip.
This also carries over into your motherboard. In this sense, AMD makes it slightly easier, as the AM3+ boards only have 3 chipsets to choose from; and while some are better for use in an OC'd system than others (i.e. choose a 990FX chipset board), you can still OC on one of the lower chipsets (i.e. 970), just not as well. Intel seems to have a ton of chipsets, some of which are specifically for OC'ing while others won't allow it at all (even with an unlocked CPU). Obviously, the Intel boards that can be used to OC your chip are more expensive, so if you're going to OC your system from the start (or are pretty certain you're going to down the road) you have to spend more cash now to make it possible.
2) What other capabilities are you looking for? For example, I have an SSD in my system, which uses one of the SATA III ports. Assuming that a) I had the cash to do so, and b) the desire to spend all that time reinstalling my system from scratch, then the only way I could "upgrade" to an M.2-based SSD would be to add an expansion card, as my motherboard doesn't come with that. However, if you plan on using an M.2-based SSD, then you should probably make sure your motherboard has a built-in port for it. Same thing for SLI/CrossFire support: if you plan on starting with it, or want the capability to do so in the future, you have to make sure your board will support it. Note that some boards will support CrossFire but not SLI, or may support Quad CrossFire but only Dual SLI. Same goes for maximum RAM & RAM per slot. Also consider how much room you want for expansion. mATX boards, for example, are cheaper & can fit into a smaller case; but they also usually are very limited in their SLI/CrossFire support (i.e. usually don't support it), & may only have room for 1 or 2 expansion cards besides your GPU. Not a problem, unless you plan on adding a sound card, need to add a Wi-Fi card, or have some additional expansions needed. Not to mention I find that mATX cases tend to have poor airflow compared to mid-tower or full-tower ATX cases, & I've had a couple of systems in the past that fried my HDD because of heat.
3) What is your budget, & how flexible is it? After answering the first two, this is where it gets down to the nitty-gritty. The primary edge AMD has over Intel is the price: motherboards tend to be roughly similar in cost (although the better Intel boards are still slightly more expensive), but AMD chips tend to be much cheaper than Intel chips. Some of that margin gets eaten away when the "common" items (case, fans, PSU, RAM, SSD/HDD, DVD-ROM, etc.) are added in, but there's usually still a little bit of a margin. Sometimes, that margin is small enough that the Intel build is really worth the slight extra cost involved. Sometimes, however, the margin is enough that you can improve your build: maybe it lets you add an SSD when you couldn't afford it before; maybe it lets you pick a better GPU than you could with the Intel build (which, quite often, will have much more of an effect on your gaming experience than the CPU choice); maybe it just lets you save back some money to get a couple of new games you've been dying to try for a while; or maybe it lets you take your spouse/significant other on a special date to thank them for letting you get the new system.
In short...if your budget is limited, an AMD build can help you build a system that can still provide decent performance. If your budget isn't limited, then go for an Intel build -- but pick a Skylake build for future growth. If you can hold off for now...then wait until Zen comes out to see how it compares performance- and price-wise to Skylake.