Consider:
Cl2 is an oxidizer. Cl has an oxidation number of 0. This is unusually high for chlorine which is usually -1. Maybe not a great order of magnitude, but it is not the usual oxidation state of chlorine. Therefore it is unusual. Unusual doesn't necessairly imply a radical magnitude difference, although I could see where one could imply that from what I wrote.
Secondly:
As far as I'm aware, sulfuric acid isn't a powerful oxidizing agent; it is a powerful dehydrating agent, though. You may be thinking of nitric acid, Mitch, which is a significant oxidizer.
Perhaps this is a bit oversimplified, but for most high school classes, these are the rules used to determine the oxidation states of the hetero atoms.
1. All elements are in the 0 oxidation state in their elemental form
2. Alkalis are always +1
3. Oxygens are usually -2, although can be -1 in peroxides and fractional in superoxides.
4. Hydrogen is usually +1 although can be -1
5. Most other elements are the charge you would expect from the periodic table, however you must achieve charge balance, and therefore these elements can be of differing oxidation states.
Now, that being said (and that was off the top of my head, so it may not be complete), there are some more complicated situations that arise when several atoms of the same type have different oxidation numbers, such as Fe3O4. (Fe(II) and Fe(III) mix).
Going on what most HS students are taught:
Sulfur in sulfuric acid is in the +6 state.
Sulfur in K2S2O8 is +7 as Mitch said, and is +2 in Na2S2O3 as he also stated.
Thus, potassium peroxydisulfate is a more powerful oxidizing agent than sodium thiosulfate.
Although the situation is more complicated than that if you look at the structures of these compounds, I would not expect a HS student to understand any more than that. If someone wants to post a structure, we can go into more detail, but the underlying idea that one of these materials is more oxidizing based on average oxidation number still works.