I got an answer to this offline. The answer is that the form looks the same for all representations with a suitable redefinition of the star product. For example, in the Husimi Q representation, we can define a new kind of star product as follows:

$
f\circledast g= f \exp \left ( {{\frac{\hbar }{2}}(\stackrel{\leftarrow }{\partial }_x
\stackrel{\rightarrow }{\partial }_{p}+\stackrel{\leftarrow }{\partial }_{p}\stackrel{\rightarrow }{\partial }_{x})} \right ) \star g = f \exp \left ( {{\frac{\hbar }{2}}(\stackrel{\leftarrow }{\partial }_x-i\stackrel{\leftarrow }{\partial }_{p})(\stackrel{\rightarrow }{\partial }_x+i\stackrel{\rightarrow }{\partial }_{p})} \right ) g
$

If $T$ is the map from Wigner to Husimi, then this product has the following property:

$
T(f \star g) = T(f) \circledast T(g)
$

Therefore the quantum Liouville equation in the Husimi representation is

$
\frac{\partial Q}{\partial t} = - \frac{1}{i\hbar} (Q \circledast H - H \circledast Q)
$

See e.g. this reference.