Well i know for sure that a 3870 will play Crysis on Full settings at 1680x1050 which is a 20" screen. Your resolution is for a 19" monitor so I am sure that it will play Crysis very well on full settings :)
yeah, you should be able to manage at least 30-40 fps on max settings. There are alot of charts out there comparing 3850 vs 3870 vs 8800gt (256mb) vs 8800gt (512mb).