which one is better? crossfire or just a single card on same budget to get better performance?
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Depends on the budget mostly better state the budget for the entire system.
If you already have a mobo and PSU that can support crossfire and your budget is enough for at least 2 x 5770s then you will normally get better performance for your money when using crossfire but you need to look at exactly what options you have in your budget.
The 6850 shouldn't be much more then the 5770, and provides a 6970/5870 level experience for less cash. If you want to CF cards, the 5770/6850 should be the cards to go to.
It depends on what games, the rest of your components (board, PSU, monitor) and your budget. Some games aren't optimized with dual cards like WoW. Dual cards are consumes more power than single card and produce more heat/noise.