I own an RX 470 and RX 570, also a Vega 56, 980 Ti, 1080 Ti, and in the recent past a Radeon VII, so a decent range of performance there. The RX 400 and 500 series are nice, but the 460/560 are bad purchases, and the 480/580 are so close in price to the 470/570 but quite far ahead in performance, so I always recommend to make the jump if you’re going with that range - these cards stomp the Nvidia equivalent, so don’t become one of those guys who scams himself into buying a 1050, 1050 Ti, or even a 1060 
I’d also recommend 8GB variant over 4GB regardless.
However… that prebuilt is a bad deal. Zen 2 / Ryzen 3000 is announced and very close to dropping, so Ryzen 1000 and Ryzen 2000 prices are about to hit rock bottom, and you can already get a 6 core 1000 series chip for like $60-80 which is madness considering prices for even a dual core 2 years ago. If you build it yourself, that exact build is fine, and will probably cost you closer to 400EUR than 600.
Further, your current CPU while really starting to age now, is actually fine for a lot of modern games at the performance level you’re targeting (I would guess like 1080p60 maybe 1080p120 from your current specs), it’s your GPU which is gonna be holding you back, like @Wolveix mentioned. Here’s the problem, your 780 Ti on paper is really out of date, but when it comes to actual performance it’s only within 10% of the RX580, and the GTX 1060. It’s hard to justify an upgrade, even though you’ve only got 3GB memory and you’re like 6 generations behind, it is the best card of its generation.
Here’s the move I would do with your current system to maximize price:performance ratio. I would buy a used i7 4770K which you can probably get for like 75EUR, slap an overclock on that bad boy. I would then wait for Navi (almost dead on arrival but still)… to drop in July and buy a Vega 56 which is not only really well priced right now, but will be even better priced in July when Navi lands. For below 300EUR you can easily double your current GPU performance, while getting a nice little CPU uplift (10-30% depending on OC in single thread, way higher in multi thread thanks to hyperthreading) to keep you going another year or two.
Edit: I would also recommend going used on the Vega 56 purchase too, but I understand if you don’t like the idea (although 90% of my hardware purchases nowadays are used and I’ve never had a single problem). 100% sell your existing CPU and GPU on the used market once you’ve done the upgrade, as you will recoup quite a bit.
