Logic has to do with rational understanding. Ability to think clearly, and depends on one’s intellect. It is the fabric of being; How it is. It cannot be changed.
Common sense is attached to more than the wiring of the brain. It is the sensory connectivity of everything throughout the human body, including the brain.
As it leans on more than just one aspect it can be impacted by other things such as the nervous system, hormones, etc.
It is circumstantial and thus dependent on historical and geographical rootedness, culture(food), exposure, and socio-economic status.
Thus, it is something that can be improved with training, experience, and ultimately slow rewiring of the brain. The food that goes into your body changes how your body functions but cannot rewire the genetic brand of its functionality; which is rooted in your gene pool and is partly geographical (the complexity of and immediate interaction between the various molecules).
One can adapt, to changing circumstances, but still function differently.
Is it possible for logic to collide with common sense? Logic and common sense are not the same.
Someone clumsy can learn how to cope with that fact, i.e work around that attribute but will always keep that aspect of himself.
The imprint of both aspects is different and gender-based. Difference; the wiring of the brain already varies from person to person but is also gender bound. Something can be straightforward to one but complex to another.
Nature is logical and does not always make sense.
Being more logically inclined can be rigid but a stable factor whereas having significantly more common sense than logic grants you more flexibility, and resilience thus better navigation but not necessarily limitless.
Ideally, we want to have both aspects in a balanced manner; superpower.