Correct order of bond length is:

Given the nature of the $\mathrm{P}-\mathrm{O}$ bonds in both molecules, it can be deduced that ${\mathrm{P}}_4{\mathrm{O}}_{10}$ is $\mathrm{P}-\mathrm{O}$ bond length is shorter than ${\mathrm{P}}_4{\mathrm{O}}_6$ is due to the existence of double bonds.
As a result, the $\mathrm{P}-\mathrm{O}$ bond in ${\mathrm{P}}_4{\mathrm{O}}_{10}$ is weaker than that in ${\mathrm{P}}_4{\mathrm{O}}_6$.
$\mathrm{P}-\mathrm{O}-\mathrm{P}$ bond has greater % p-character in ${\mathrm{P}}_4{\mathrm{O}}_6$ as l.p. on P has greater %s-character
Thus, the option C is correct.