One of the few rules in counted cross stitch is that all the stitches should go in the same direction. It doesn't matter if the bottom half goes "/" and the top goes "\", or vice versa. Just make sure that every stitch in the project is done the same way. And to be perfectly honest, there are exceptions to this rule such as 3/4 stitches.
The direction a person first learns to stitch seems to be a regional thing. The only reason it might be of importance is if you choose to do a very complex chart. Some complex charts with many fractional stitches or other embroidery stitches exhibit a subtle bias, assuming that the X's will be done a particular direction.
Stitchers who use the traditional method complete each X as they go:
Stitchers who use the Danish method do the bottom stitches first, and complete the X's as they return:
Many people use a mix of the two methods. They may use the Danish method for most stitches, but do the occasional isolated stitch as a complete X. Another school recommends doing rows with the Danish method and columns with the traditional method. This causes the thread on the back to make vertical lines.
Apparently, some antique samplers which were done in the traditional method survive today because the X's hold the fabric together, and the thread forming the X's themselves is less stressed. The "one-X-at-a-time" approach works well when stitching over one thread, rather than the usual two, as it helps stop the thread from disappearing behind the fabric.
Many people find the Danish method to be faster, and to result in less confusion about current location.
Choose a method which you like, preferably one which results in neat backs. While a neat back isn't required for a good looking front, it usually helps.