It is always less expensive and there are a lot less issues when Building Out. Prior to building out you will need to check your local municipality's Setback Requirements. These requirements dictate how closely your are able to build to your property line. Some municpalities do allow you to get a variance (special permission) to construct outside your setbacks. If you are unable to build out due to your current foundation plan, maximizing your setbacks, then you will have to build up. The costs to Build Out are less expensivie due to the project usually being more straight forward and issues connecting the two structures are minimal. An Architect may charge you more for Building Up due to the extra labor required for them to engineer (Structural Engineering) a new structure on top of the existing. There may be extra costs to strengthen the existing footers for the additional load of the new structure or new reinforced support posts and beams may need to be added. The Contractor is definitely going to charge more and probably "pad" their estimate due to the "unforeseen" issues that may exist. There may also be an "unforeseen" clause in their estimate and as a result the project could cost a lot more than the original agreed upon cost for the project. Most likely this can be expected until the industry develps "X-Ray Glasses" to see into the existing walls and roof. You may have the additional costs of storing the furniture located in the rooms below the new structure and due to the size of the project you may need to temporarily move out. Other "natural" factors may affect the construction costs of the project when Building Up. It is often very difficult to protect the open area of construction from weather conditions and rain/water damage can occur. You will always want to have a clause in your Construction Agreement dictating the terms as to which party is to cover such issues.
Build out whenever possible... less expensive & less "headaches!"