Why is Nitric Acid more reactive and caustic than Sulfuric or Hydrochloric?
Nitric Acid is indeed what most often is referred to as a "strong acid" (at ambient temperatures), and its $\mathrm{pK_a} \approx -1$, i.e nitric acid in diluted solution is almost always fully dissociated except in extremely acidic solutions. 

First of all, how does it compare to other "strong acids", for example sulfuric acid

$\ce{HNO3 + 2 H2SO4 ⇌ NO2+ + H3O+ + 2HSO4−}$

Clearly, in this reaction sulfuric acid acts as the "acid", while nitric acid acts as the "base", hence sulfuric acid is indeed a stronger acid.

Reactions of dilute nitric acid with some metals are typical of an acid, namely:

$\ce{Mg + 2 HNO3 → Mg(NO3)2 + H2\uparrow}$

Other metals that react in this fashion are manganese and zinc.

You do correctly note that a special feature of nitric acid's reactivity is its strength as an oxidising agent, and this is also evident in its reactions with metals, for example. However, do note, that the exact details depend on the concentration of the acid and the nature of the metal

For example, nitric acid can oxidise non-active metals such as copper and silver, however, the products depend on temperature and the acid concentration.  

For instance, copper reacts with dilute nitric acid at ambient temperatures with a 3:8 stoichiometry:

$\ce{3 Cu + 8 HNO3 → 3 Cu^2+ + 2 NO + 4 H2O + 6 NO3−}$
The nitric oxide produced may react with atmospheric oxygen to give nitrogen dioxide. 

However, with more concentrated nitric acid, nitrogen dioxide is produced directly in a reaction with 1:4 stoichiometry:

$\ce{Cu + 4 H+ + 2 NO3− → Cu^2+ + 2 NO2 + 2 H2O}$

Metals like chromium, iron and aluminium readily dissolve in dilute nitric acid, but the concentrated acid forms a metal-oxide layer that protects the bulk of the metal from further oxidation; thus, concentrated nitric acid serves to passivate these metals towards further reactions. Common metals that are passivated by concentrated nitric acid are iron, cobalt, chromium, nickel, and aluminium.