It would appear that the one you say is compatible is well obsolete as it was introduced in 2006 as opposed to the one you have which was introduced in 2010
Type CPU / Microprocessor
Market segment Desktop
Family Intel Core 2 Duo
Model number ? E6600
CPU part numbers HH80557PH0564M is an OEM/tray microprocessor
BX80557E6600 is a boxed microprocessor
Frequency (MHz) ? 2400
Bus speed (MHz) ? 1066
Clock multiplier ? 9
Package 775-land Flip-Chip Land Grid Array (FC-LGA6)
1.48" x 1.48" (3.75 cm x 3.75 cm)
Socket Socket 775 (LGA775)
Introduction date Jul 27, 2006
Type CPU / Microprocessor
Market segment Desktop
Family Intel Pentium Dual-Core
Model number ? E6600
CPU part numbers AT80571PH0832ML is an OEM/tray microprocessor
BX80571E6600 is a boxed processor (English version)
BXC80571E6600 is a boxed processor (Chinese version)
Frequency (MHz) ? 3067
Bus speed (MHz) ? 1066
Clock multiplier ? 11.5
Package 775-land Flip Chip Land Grid Array (FC-LGA8)
Socket Socket 775 (LGA775)
Size 1.48" x 1.48" / 3.75cm x 3.75cm
Weight 0.8oz / 23.3g (CPU)
11.8oz / 335g (box)
Fan/heatsink E33681-001
Introduction date January 17, 2010