People's preferences are usually dictated by their environment's and whether or not they have a dedicated space to dry and cure.
You want things to be around 70-75 degrees with the humidity around 40%. Not everyone has a room that has these temps and RH though, so they use the leaves to compensate.
I personally do not have a drying room anymore, and humidity where I live is pretty much never over 15%. This is why I leave the fan leaves on, it slows the drying process a tad because it's extra moisture in the plant that needs to be removed. If I removed all the leaves my plants would dry in like 2 days, WAY too quick. By simply leaving some leaves on, I extend the drying time to 5-6 days. Perfect.
Conversely, if I lived somewhere like Florida with excessive humidity I would be removing every single leaf on the plant. A fan for airflow also becomes much more important the higher your environment's humidity is.
This is why you see some people doing different things. Some people remove nothing at all, others only remove fan leaves, others do a full blown trim job before hanging.
It really just depends on your ambient RH and temps and doing what it takes to ensure drying takes ~7 days without causing any problems.