There are basically two considerations when making a cheese sandwich that will satisfy..
Coverage and overlap.
Coverage is the ratio of unexposed vs exposed bread, and overlap is the percentage of double layering needed to cover areas exposed by uneven cheese coverage. Coverage should be maximised and overlap minimised (for sandwiches within the ISO9002 specification, what you do with non-standard sandwiches is of course entirely your own business).
Thus, horisontal or vertical layering by itself makes no difference to the ultimate value of the sandwich except that the pattern employed should achieve the desired coverage with minimal overlap & wastage. Note that my canine of the sausage persuation disagrees entirely with this postualate as she is usually the sole beneficiary of the offcut process, but usually I find the perfect orientation of the cheese to be entirely dependent on the shape of the specific cheese & bread under consideration.
If longer, thinner vertical strips will achieve better coverage than shorter, thicker horisontal strips then so be it. Sometimes diagonal patterns cover the bread better, but might require lots of smaller cuts to optimise overlap (that gets my dog excited). The aim remains to achieve optimal coverage & minimal overlap within the parameters of the size & shape of the bread & cheese.
Overhang, crust disposal and the practice of simply folding a slice of bread around a block of cheese before chomping down is considered out of scope for this discussion.
