I have tried a range of different voltages before. While the level of voltage can affect the degree of separation among bands (e.g., band broadening at low voltage), I've never observed "rank changes". What I mean is that heavier molecular weight bands always migrate more slowly than lighter weight bands (assuming no effect of comformation - I'm not sure whether voltage can affect DNA conformation within the usual range for electrophoresis).
W = V x A, so the above applies to wattage. However, I don't have any experience with altering amperage.
Voltage (or amperage) should not affect the relative migration of bands, provided that it is homogeneous (if the electric field is not homogeneous, you can for example observe "smiling" gels, with DNA migrating faster at the center of the gel compared to edges) . In my experience, what can affect the relative migration of bands is the quantity of DNA in the wells (if there is a large difference), or differences in loading dye concentration among samples.