Considering the standard rolls, is there any reason to pick 13 for Constitution instead of 12? Or similarly, is there any reason to pick 13 for Intelligence instead of 12?

I'm currently creating an half-elf bard, and I can pick 12 (+1) Constitution and 13 (+1) Intelligence. Considering the backstory I thought for him, he would be more logical - he's meant to have spent half his life learning magic but never being able to actually concentrate on the study, yet he's physically weak. 

However, I then realised this is quite the silly thing, since both are "rounded down" and only provide a +1 bonus. Making 13 (+1) and 12 just "better" with no draw back?