afaik the 4870 is actually faster than the 5770. So in really it would hardly be an upgrade at all. Look on ebay for a cheap 4890 or a gtx275. My first 3 graphics cards were ebay cast-offs.
The other option is if you can find a cheap 4850 and crossfire them. I'm in the same boat looking at an upgrade but I think my ageing socket 939 dual core and motherboard will come first.
If you're going to want dx11 and a higher resolution then i'd opt for the 5770 or possibly the 5850 if you can afford it. If you're not going for a higher resolution i'd still opt for a newer card as it'll be a good investment.
your only gaming at 720 and the 4850 is struggling that surprises me alot. you tried reducing AA from 8x to like 2x. As most of the benchmarks ive seen the 4850 gets 40-60fps in most games at that resolution. 4850 to 5770 is like upgrading to 4870 from 4850 you wont notice alot of diffrence. the mith that the 5770 will actually play a true direct x 11 game at above 1280x1024 is one that needs dispelling. battleforge a true direct x 11 game gets 37 fps avr at 1280x1024.( very high settings and 2x AA you need very high to even enable the direct x 11 features). at 1920x1080 it scores a dismal 18fps. in what most would consider a very none taxing game. power consumption is brilliant but do we really care for a cheaper power bill. most people arnt running a 5770 on a 430 wat psu to make any use of the savings it offers. Ive seen some peoples specs with a 700 watt psu and a 5770. You are not saving electric there your using more lol. 4850 in crossfire is a nice upgrade. and cheap ( £60-£90 ) and is a bigger upgrade than any other card you can really get including the 5850. 4850 crossfire gives close to 5870 performance.
While I agree with most of what you say Rollo, there's one key issue. Just because you have a 700W PSU, doesn't mean it'll use 700W. Rather it'll provide the power needed by the components along with a percentage of energy loss due to the PSU's inefficiency. In a all cases efficiency varies according to the load put onto a PSU, as a result it can be better in the long run to have a PSU running at around 40%-60% load to get the maximum efficiency. For example: No matter what PSU you use, the 5770 will create power savings over something like a 4870. The issue here though is cost more than anything as the 650W PSU is more than adequate for pretty much all single-GPU setups. As I said from the start a 5850 (or equivalent) is required to create a noticeable difference and even then it's overkill for a 720p resolution. (It would help considerably if Penryn 2 Hertz were to reply to this to see why they thought it necessary for an upgrade *hinthint* )