Well I believe that each depend on environment, time and reason.
If you live in a particularly humid region you would benefit from the extra air flow of a mesh and if you want a slower dry you would string em up, so:
Mesh
Pro
More organisation if growing multiple strains or a
very large amount
Grey area
Faster dry (especially if there is a fan under or nearby)
Con
Extra abrasion on buds so some crystal loss is a possibility
$$$
Some can be quite big and take up space
Need a relatively secure spot to place it that also allows for its shape
Inattentiveness can take you out of cure zone
Hang
Pro
If you have a space to grow you have a space to hang
String is relatively cheap and you could have some left over from training to use
Very little contact from cut to container
Grey area
Slower dry, this can be beneficial for low humidity
Con
Slower dry for humid zones can allow mold
There may be a lack of space if growing a large amount
Less organisation
Knot tying skill may be needed based on amount
It all comes down to the space you're drying in and if it's for you or if it needs to go out the door as soon as possible. Maybe try a test batch on it next time you can use it and see what you prefer.