[tex]x=2^{2008}-2^{2007}-2^{2003}\\
x=2^{2003}(2^5-2^4-1)\\
x=2^{2003}(32-16-1)\\
x=2^{2003}\cdot 15\\
\\
y=3^{2006}-3^{2005}-3^{2003}\\
y=3^{2003} (3^3-3^2-1)\\
y=3^{2003}(27-9-1)\\
y=3^{2003}\cdot 17\\
\\
3^{2003}\cdot 17 \ \textgreater \ 2^{2003} \cdot 15\\
\boxed{y\ \textgreater \ x}[/tex]