Well resolution is actually key about graphical cards performance(fps) . If you're using 1024*768 resolution, so far you have big advantage for performance. For example, I can have 40fps performance with 6850 card at 1920*1080 res, but you can also have 40fps, with your 4870 card at 1024 res. So far so good.
If you are talking about next gen, then technology may start to be a handicap on some games. For example you can never use Dx11 with 4870, it has opengl 3.2 and shader 4.1.
Summary: Yep if you can afford to buy 6850, it would make huge difference. It's a great card. I'm using it with 1680*1050 res. And I'm having great fps in all games at high graphical settings. So it means you will have even better fps with 1024 res. So you will have pretty more time than me to start complaining about fps ratings at high settings.
I think you can't play all next gen games at medium sets, you may need to drop to low sets for some of them at 1024 with your 4870.
I think best solution for you would be to sell your card and add money to it then buy secondhand 6850. Because there are lots of 6850 users whom also wanna upgrade their cards.