TRUE is correct, and here's why:

The extent to which charged particles are deflected in an electric field depends primarily on two factors: their charge and their mass. While it's true that $\alpha$-particles (which are helium nuclei consisting of 2 protons and 2 neutrons) carry a larger charge (+2e) compared to $\beta$-particles (which are high-energy electrons or positrons carrying a charge of -e or +e), the mass of the $\alpha$-particles is significantly larger than that of the $\beta$-particles. Specifically, an $\alpha$-particle is roughly 7300 times more massive than a $\beta$-particle.

The force exerted on a charged particle in an electric field is given by $F = qE$, where $F$ is the force, $q$ is the charge of the particle, and $E$ is the electric field strength. While the force acting on an $\alpha$-particle is greater due to its larger charge, the effect of this force (in terms of acceleration, given by $a = F/m$, where $a$ is acceleration and $m$ is mass) is much less significant for $\alpha$-particles because of their larger mass.

$\beta$-particles, being lighter, experience a greater acceleration for a given force, which results in a more pronounced deflection in an electric field despite their smaller charge. Thus, the key factor in the deflection of charged particles in an electric field is not just the magnitude of their charge but also their mass and the resulting acceleration from the force experienced in the electric field.