Will SnO2 or SnO form from this reaction?
The actual reaction of tin (II) chloride with water in the presence of air is given here.

$$\ce{6SnCl2 + O2 + 2H2O → 2SnCl4 + 4Sn(OH)Cl}$$


  Tin(II) chloride react with oxygen and water to produce tin(IV) chloride and hydroxotin(II) chloride. Interaction with oxygen and air humidity. This reaction takes place slowly.


As Mithoron noted, the reaction takes place very, very slowly and thus get hydrolysed partially to form the basic salt, $\ce{Sn(OH)Cl}$ instead of forming the hydroxide or the oxide.

The basic salt will also form when tin (II) chloride reacts with water in the absence of air, thanks to Gannex.

$$\ce{SnCl2 + H2O ⇄ Sn(OH)Cl + HCl}$$


  Tin(II) chloride react with water to produce hydroxotin(II) chloride
  and hydrogen chloride. This reaction is proceeds by diluting the
  solution tin(II) chloride. (source)


As noted earlier, the reaction is very, very slow and maintains an equilibrium between the reactants and the products.

However when tin (II) chloride is present in a concentrated, acidified solution, it will form a complex.(source)

$$\ce{SnCl2 + H2O → [Sn(H2O)Cl2]}$$


  Tin(II) chloride react with water to produce dichloridoaquatin.
  Tin(II) chloride - concentrated solution. pH &lt; 7.