Why is the electric component of a light field more important than the magnetic component? This is the common impression.
But, is it just a rule of thumb and correct only in some wavelength region or does it hold universally? 
 A: It is more important in the sense of accelerating charged particles.
In vacuum, it is easy to show that the ratio of the amplitudes of the electric field and magnetic field is $c$ (in SI units).
The Lorentz force on a charged particle is
$$\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})$$ 
If we just consider the magnitudes of the electric versus the magnetic forces acting on a charged particle, then (for a charge in vacuum), we can see that
$$ \frac{F_B}{F_E} = \frac{v}{c}$$
Thus unless the charges are moving relativistically then it is the electric part of the Lorentz force that is dominant.
In a conducting material, the balance between electric and magnetic fields changes. In a very good conductor then then
$$\frac{E}{B} = \left( \frac{\omega}{\mu_0 \mu_r \sigma}\right)^{1/2} = c\left( \frac{\omega \epsilon_0}{\sigma}\right)^{1/2},$$
with a a phase difference of $\pi/4$ between the E- and B-fields. In general this ratio will be $\ll c$ in a good conductor where $\sigma \gg \omega \epsilon_0$.
