HD 7850's are around the £200 mark while the 6870 is nearer £100. The raw specs of the card show little difference so is the performance that much more of an increase?
If you look at the benchmarks in this article many compare both http://www.anandtech.com/show/5625/amd-radeon-hd-7870-ghz-edition-radeon-hd-7850-review-rounding-out-southern-islands/
BTW 7850 £160 http://www.pixmania.co.uk/uk/uk/12687749/art/vtx3d/radeon-hd-7850-x-edition.html 1Gb version (also a budget brand) 2Gb can be found under £180. You can also find 560Tis and 6950s inbetween these prices and inbetween in performance. It really depends on how much the price matters to you but I would say the 6870 is best performance for the money if you want more you have to pay for it. The 6870 can play ultra settings in all but the most the most demanding games 1920x1080 but the 7850 most likely still will in a year.