First things first. Let’s start by defining these concepts. According the Merriam-Webster dictionary, Logic is defined as a science that deals with the principles and criteria of validity of inference and demonstration: the science of the formal principles of reasoning. Therefore, logic always depends on facts to draw conclusions.
Common Sense by definition is, sound and prudent judgment based on a perception of the situation, experience or fact. As it relates to perceptions, common sense is not always accurate and can sometimes be based on assumptions, social acceptance more than truth.
Logic is used to reach a conclusion using the most accurate path available. Talking about logical thinking means a way to analyse a problem to find an answer sometimes using a formal system similar to mathematics (a process / disciplined method of thinking) to help us to reach a conclusion which is as accurate as possible. Logical thinking is a process which should involve no facts based on emotion.
Some Main Differences
Common Sense:
is a stereotype and assumptive.
cannot be reproduced by others, even with all the truths.
is, mostly, emotions.
Logic:
is calculation – based on collected facts.
can be reproduced by others (given all the facts).
Doesn’t care about emotions… even when there are emotions in the equation, it’s just a data point.
The main reason some people think there’s Yours and Mine logic, is, there’re missing facts that cause inconsistency with two people’s logical conclusions, and some people think Logic is Reasoning. Of course this topic can be explain with much more complexity, but my goal is to keep it simple.
Probably we could conclude that logic is more important than common sense, but not too fast.
When a society lacks common sense, absurd and irrational things can happen and, as a result, chaos and social disruption will prevail.Â
In his article,Early to Rise Lifestyle: The Importance of Common Sense, author Robert Ringer explains:
You don’t need to be a Ph.D. to exercise common sense. It’s a trait you develop through purposeful awareness and habit.  And I would add to that that in order to be aware and develop a habit requires self-discipline, the self-discipline to do the right thing rather than doing what makes you feel good at the present moment.
Common sense equates to wisdom, whereas an academic understanding of specific areas of life equates to knowledge. Â In simpler terms, what common sense boils down to is a sound understanding of how life works. Â This requires that a person learn through his experiences and not delude himself about the causes that lead to his consequences.
Having said this, I believe that most people have a reasonably good understanding of what is the right thing to do in most situations. Â In other words, they know the difference between responsible and irresponsible actions.
The problem, however, is that too many of these same people – at the moment of truth – have a habit of ignoring their intellect and instead acting on emotion.  That, again, is where self-discipline comes in.  I can’t stress it enough:  All the common sense in world is useless if one doesn’t have the self-discipline to apply it.
I believe that what we need more than anything is discernment. It will be times that logical thinking is what is needed it and others, common sense. Knowing when to choose the appropriate one, there is wisdom.
What are your thoughts?