Benefits of including short and/or long-term visits abroad on my CV?
I don't see any drawbacks adding your grants and visits in CV, but it will surely increase the weightage of your CV in this competitive world. I have been a Travel Grant Reviewer since last 5 years to select suitable candidates to attend the meetings/conferences. My experiences give the following merits to add them in CV.


Grants/Awards/Prizes proves your ability to be considered in top researchers. 
Visits abroad proves your ability to work in different environments/places and with different peoples. 
Listing your conferences and presentation details proves your ability/interest to present your work in the international forum.


So all the points have their own meaning to define your potential. If you don't mention them, then how do you think that you will be evaluated properly?