Note that most radical mechanisms do not explicitly feature homolysis of $\ce{C-H}$ bonds or $\ce{C-C}$ bonds. If one were to compare these two processes, say for ethane $\ce{CH3CH3}$, we would find that homlysis of $\ce{C-C}$ is favored over homolysis of $\ce{C-H}$. Obligatory bond dissociation energy references for the organics and here for the halogens.
Homolysis
$\ce{C-C}$
$$\ce{H3C-CH3 -> 2H3C.}\ \ \Delta H^\circ=377\ \text{kJ/mol}$$
$\ce{C-H}$
$$\ce{H3CCH2-H -> H3CCH2. + H.}\ \ \Delta H^\circ=423\ \text{kJ/mol}$$
However, $\ce{C-C}$ and $\ce{C-H}$ homolysis steps are not common steps in radical mechanisms of alkanes. For example, the chlorination of ethane begins with the homolysis of $\ce{Cl2}$, which is much more favorable than homolysis of $\ce{C-C}$ or $\ce{C-H}$.
$$\ce{Cl2 -> 2Cl.} \ \ \Delta H^\circ = 243\ \text{kJ/mol}$$
The chlorine radicals then react with the alkane by abstraction, meaning that bonds are being formed as well as being broken.
Abstraction
$\ce{C-C}$
$$\ce{Cl. + H3C-CH3 -> Cl-CH3 +H3C.}$$
$$\begin{array}{c|c|c|}
& \text{Broken} & \text{Formed} \\ \hline
\text{bond} & \ce{H3C-CH3} & \ce{Cl-CH3} \\ \hline
\Delta H^\circ & 377\ \text{kJ/mol} & -350 \ \text{kJ/mol} \\ \hline
\end{array}$$
$$\Delta_r H^\circ = +27 \ \text{kJ/mol}$$
$\ce{C-H}$
$$\ce{Cl. + H3CCH2-H -> Cl-H +H3CCH2.}$$
$$\begin{array}{c|c|c|}
& \text{Broken} & \text{Formed} \\ \hline
\text{bond} & \ce{H3CCH2-H} & \ce{Cl-H} \\ \hline
\Delta H^\circ & 423\ \text{kJ/mol} & -432 \ \text{kJ/mol} \\ \hline
\end{array}$$
$$\Delta_r H^\circ = -9 \ \text{kJ/mol}$$
Thus, abstraction of $\ce{H}$ by $\ce{Cl.}$ is more favored because it is coupled to the formation of the $\ce{H-Cl}$ bond.
