Id say a 6850 is about equivalent on the dx11 side, really the 4890 performance should lie somewhere between the 5770 (6770) and the 6850, the 6850 would be a good upgrade imo if you are trying to keep the same performance and a little better and it draws much less power and creates much less heat the 4890
some would say the 6790 is closest in performance but that card represents bad price/performance imo although it is likely the closest thing to 4890 performance also the 5830 is similar, in the end get a 6850
A Radeon 5870 remains a very powerful card despite being a generation old, easily outperforms the 4890, and can be found for about $200... if you can find it. AMD doesn't stock retailers with it anymore, so you would have to buy it from a non-major seller (IE from someone on Ebay, etc.) The 5850 also outperforms the 4890, if to a lesser degree, but like the 5870 you will probably have trouble finding it in stores.
The 6850 is about equivalent performance, if not slightly more than, to the 4890, and you have the benefits of it being a card in the most recent generation and being in stores. That goes for about $150. The 6870 is another step up (about where the 5850 is compared to the 4890, IIRC) for about $180.
yeah 6870 makes more sense for an actual 'upgrade' when you can get a 6870 for around 170 new I dont think its worth it to get a 5870 at 200, personally im on ebay a lot and most 5870s are selling for way beyond there performance imo (250+) if you can find one for cheap go for it, its a great card dont get me wrong but I think the 6850/6870 would be a good choice..
Like others said, Radeon 6770 series is comparable but has about half the memory bandwidth than the 4890 since it is 128-bit wide bus GDDR5 vs 256-bit. Same number of shader/stream processors.
Memory bandwidth is critical on high resolution rendering for frame buffering. Since 1280x1024 is very low, the 6770 should be a decent substitute for the 4890 at 80% lower power.
Also look into the older Nvidia GTX 460 768MB. It has been replaced by the 550 so it can be found for under $100 in the US after MIR - not sure about NZ. 460 768MB has similar performance to a 4890 and is DX11. http://www.anandtech.com/bench/Product/175?vs=156