It depends on the size of the mudroom and how much labor is required. If you are handy with a hammer, it might be cheaper for you to build up the mudroom. But if you need to hire a contractor, it will probably be cheaper to add on the mudroom. One option that could save you some money is to build the mudroom yourself, but have the contractor install the door and windows. This will save you some money on materials, and it might also be a little bit faster since you won't have to wait for the drywall contractor or painter to finish their work.

It depends on the cost of the two options and how much work needs to be done. If it is cheaper to add on, then it would be more economical to do so. However, if it's cheaper to build up, then that would be the better option. You'll need to get a contractor in to give you an accurate estimate for the work required.