Why is nitric acid a stronger oxidising agent than sulfuric acid?
The nitrate ion is a strong oxidant whereas the sulfate ion is a milder oxidant that only shows oxidizing properties in high concentrations. The oxidizing atom in question is the oxygen atom in the acid, not the hydrogen ion. This is because hydrogen ion is not very electrophilic, which is why non-oxidizing acids cannot dissolve copper: even copper has a higher affinity to electrons than hydrogen.

In a nitrate ion, the molecular structure is inherently not very stable, as the nitrogen atom has to bear a positive charge to maintain the molecular structure. Besides, nitrogen is in itself a very electronegative element, so that makes the nitrate ion even more unstable, hence its oxygen atom readily reacts with other atoms or molecules that oxygen can oxidize, including chloride ions: 
$\ce{Cl- + O -&gt; OCl-}$ 
$\ce{H+ + OCl- &lt;=&gt; HOCl}$ 
$\ce{H+ + Cl- &lt;=&gt; HCl}$ 
$\ce{HCl + HOCl &lt;=&gt; H2O + Cl2 }$