Dry trim, wet trimming means the water/moisture must come out through the buds only and this seems to take some of the terpenes away too.
If the leaves are left on while drying, most of the water/moisture goes out through them, leaving more terpenes in the buds.
Cutting the plant up into individual branches makes for easier, faster and more even drying.
The leaves also protect the dry buds and help prevent the trichomes from being knocked off.
I usually dry trim (manicure) right before consumption and store my buds with most of the leaves left on and only remove the fan leaves from the dried buds, otherwise the buds are too hard to get them into the jars.
If you live in an area where cannabis is illegal, manicured buds could be construed as being "ready for commercial sale" whereas untrimmed buds allows you to argue that they are only for personal use. This alone could be a deciding factor in wet versus dry trimming.
Hope this helps, Organoman.