The format question is worth more than the pattern question, because it decides how fast your team can wrap and how much paper ends up in the bin.
Sheets suit fixed box sizes
If you ship one or two box sizes, pre-cut sheets win outright. A sheet cut to the box takes seconds, needs no cutter, needs no judgement from whoever is packing, and gives an identical result whoever does it.
The sizing rule is the box girth plus about two inches of overlap on the long side, and roughly two thirds of the box depth at each end. Send the box dimensions and the sheet size falls out of them.
Rolls suit variety and volume
If items vary a lot in size, or you are wrapping hundreds a day at a counter, rolls are the answer. Staff pull exactly the length the item needs, which cuts waste and removes the awkward moment where the item is slightly too big for the sheet in hand.
Match the roll width and core to the dispenser you already own. Core diameter is the specification most often got wrong, and a roll that will not sit on your cutter is an expensive doorstop.
Watch the pattern direction
On a roll, a directional design has to run the correct way relative to the pull, or every item comes out wrapped sideways. It is invisible on the flat artwork and obvious on the counter.
We set the direction on the mockup and print it on the roll label so nobody has to work it out in December.
A common compromise
Plenty of businesses buy both: rolls for the shop counter where sizes vary, pre-cut sheets for the fulfilment room where they do not. One pattern, one print run, two formats off the same press.