Here's the reason to do one versus the other:
Independent Groups:
It is easy to find subjects. It is the only design that works when you use variables such as Gender - you can't change men into women and vice versa for the second trial.

Repeated Groups:
Fewer subjects are needed.
More statistical power because:

• These designs reduce experimental error as you reduce the chance that you randomly select wildly different kinds of individuals for each group.
  
  
• Technically, you subtract a covariance term in the standard error and make it smaller. Thus, you get a bigger t-ratio and this makes it more likely that you will get significance.