New computer, or do I upgrade?

As with all things it depends on what games you want to play, and what operating system you're using. In windows it's fairly even, under linux Nvidia have better overall performance although AMD have better 'open source' driver support. Both companies get involved in supporting development of certain games, games supported by AMD tend to run better on their cards and vice versa with Nvidia.

Nvidia have a reputation for being a little easier to work with in terms of driver support, although AMD have been making improvements lately in that regard, and I've never really had that much issue with AMD drivers so I think it can tend to be exaggerated somewhat (people get so tribal about graphics cards, it always baffles me).

The comparison of the 290X and 780ti is tricky- at lower resolutions the 780ti is faster (e.g. 1080p or 1440p) however as the resolution increases the 290X holds on to more of it's performance than the 780ti and ends up ahead (mainly because it has a wider memory bus and also a larger frame buffer, both of which help at high resolutions). Note that at the lower resolutions both cards should max out pretty much any game at high frame rates. On that basis I think you'll find the 290X is going to age better than the 780ti although they're both great cards.

The reference model 290X should be avoided (the design AMD released themselves) as they used a truly dreadful cooler that was loud and didn't keep the temps low enough. Thankfully there are loads of 290X cards with custom coolers on them and they are fine. There were no issues with the reference 780ti.

There are also some 'extras' that each company's cards offer depending on what you prefer:
Nvidia offer 'PhysX' physics acceleration that is a nice extra in games that support it (adds some nice detail effects like more accurate cloth simulation, more particles from explosions and such although it isn't that widely supported). They also have things like game streaming to their 'project shield' handheld console if that floats your boat.

On the AMD side, they have added 'true audio' which allows the graphics card to process special audio effects. It looks like a great tech although not many games currently support it (the new Thief is the first, more are coming but not out yet). There is also 'Mantle' which boost the performance of AMD cards in certain games (battlefield 4 is a good example).

Personally I own both Nvidia and AMD graphics cards and I have found both work very well. My personal recommendation is get the best card you can for the money- currently in the high end cards I'd take the 290X as its a very powerful card and it's better suited to high resolution 4k screens (which are already coming down in price). That said if you really prefer Nvidia then a 780ti is a great card as well.

PS sorry for the wall of text, also RazerZ's build looks good to me- you shouldn't go far wrong with a rig like that (pretty much as powerful as you can get at the moment )