One gas bleaches the color of flowers by reduction, while the other by oxidation, the two respective gases are:

Aqueous solution of ${\mathrm{SO}}_2$ acts as an reducing agent. 

$$\begin{gathered} {\mathrm{SO}}_2 + 2{\mathrm{H}}_2\mathrm{O} \to {\mathrm{H}}_2{\mathrm{SO}}_4 + \underset{ \mathrm{nascent} \\ \mathrm{hydrogen}}{2\mathrm{H}} \end{gathered}$$                                                                   

Thus ${\mathrm{SO}}_2$ in presence of moisture is used as bleaching agent. This is due to the reducing nature of ${\mathrm{SO}}_2$. For delicate articles 

$\mathrm{coloured} \mathrm{matter} + \mathrm{H} \to \mathrm{colourless} \mathrm{matter}$

Similarly, ${\mathrm{Cl}}_2$ acts as bleaching agent in presence of moisture 

$$\begin{gathered} {\mathrm{Cl}}_2 + {\mathrm{H}}_2\mathrm{O} \to 2\mathrm{HCl} + \left[\mathrm{O}\right] \\ \mathrm{coloured} \mathrm{matter} + \left[\mathrm{O}\right] \to \mathrm{colourless} \mathrm{matter} \end{gathered}$$