In most cases either collet will work fine. However, I have had one experience with an ER16 collet that led me to rethink that statement.
I was clamping a tool with a shank diameter the same size as the small end of the collet range. It felt tight and all that sort of thing, but I was getting a poor finish and the depth of cut varied. The collet had closed up as far as it could until the slots were closed up and was not gripping the tool with full force. I had several other collets the same size and manufacture that worked fine. I retired that collet to a bag with a note not to use the small end of the range. Since then I have made it a practice to always use the smaller range when faced with a situation like you propose, that is use the 5-6 collet. This makes sure that the collet is gripping with full force and not bottoming out on it's slots making me think that everything is OK. It might never happen again, but this way I know for sure.
Gail in NM,USA
Edit. After the second pot of coffee, I corrected the text to show what I actually do. I typed it backwards which would lead to the incorrect result. Sorry. Gail.