I prefer to trim fresh as they're standing out straight and easier to trim. I typically give a good watering before I chop to slow the drying down a few days. Also get some nice scissor hash when you trim fresh.
As ProfPS said though, if humidity is low, may want to leave them a bit. I also have a friend who prefers to smoke in joint form. He leaves a lot of the sugar leaf on to keep the bud from getting too sticky when he rolls it up. The more leaf you leave behind though, the more the overall taste changes.
My suggestion, do one of each and form your own opinion based on personal preference, as either way can still be enjoyable. If you only have one plant, trim fresh and leave two or three branches to trim after drying. Should give you a small representation of both ways.