This depends on what is actually involved in the addition. It is certainly easier to build out if that makes sense for the plan to work. However you are incurring the cost of a new foundation which you already have if you go up. However if new point loads are coming down from above you may need to modify the foundation or provide new footings columns and beams to allow for these new loads. You need to start off with an architect to layout the most economical solution that also makes sense for you project and your needs. Good luck!
That question is not as simple as you present it. You need to determine what makes sense for the end use. If you just add on you incur the cost of a new foundation, do you want more basement space? or just a crawlspace?
Do you want to open up a large opening to this new space, how is the space used?
If you build up you are reusing the foundation however is the the foundation suitable for a second floor? Usually it is, but you may have new point loads coming down from the roof (which will be new in both instances up and out) and due to the configuration of what you are doing on the second floor. You really should hire an architect to discuss you needs and have him/her determine what makes the most sense economically and functionally.
Good Luck!