What is the difference between Intel Core 2 Duo & Dual Core & Which one is better for processing ?

There is only difference in name but not in functionality. 

• Dual Core is simply a generic term referring to any processor package with two physical CPUs in one, made by any Company.
• Core2 Duo is again the Brand name of Processor-Chip with two Cores (Processors) made by Intel.

Dual core processors are those that contain2 cores in a single silicon chip while Core2 Duo is the name given by Intel to its second batch of dual core processors.