Yes, I think 4-2-2-1-1 is a little bit more defensive than 4-2-1-2-1 therefore counter attack will work better with that. It depends on the opponent's formation and your team's strenghts.
eg if he has DMCs you may consider 4-2-1-2-1 if he has AMCs and Forwards then 4-2-2-1-1 would be better.
Or if you have strong MR-ML go for 4-2-1-2-1, if you have a strong AMC go for 4-2-2-1-1.
The most important thing to play with counterattacks is to have defensive mindset.