Hock rearrangement of hydroperoxides
The main parts of the mechanism that will affect the rate of the reaction are the following steps (full mechanism on Wikipedia): abstraction of a hydrogen to form a benzylic radical and the rearrangement of the of the protonated peroxide.
These steps will be slower as they involve the formation of the higher energy species when ethylbenzene is used.


  


Secondary benzylic hydrogen have a higher bond bond dissociation energies ($357.5\: \mathrm{kJ\: mol^{-1}}$) than tertiary benzylic hydrogen ($353.3\: \mathrm{kJ\: mol^{-1}}$)$^{[1]}$. This will diminish the rate at which the initiation step proceeds, though a difference of $4.2\: \mathrm{kJ\: mol^{-1}}$ shouldn't make or break the reaction.


  


The formation of a primary carbocation would otherwise be highly unfavorable, except for that it is bonded to an oxygen atom. A lone pair on the oxygen can therefore be shared with the carbocation, thereby stabilizing it. This step will have a higher activation energy, but likely all that will be necessary for this reaction to occur is a little more heat and time.



[1] Baciocchi, E.; D'acunzo, F.; Galli, C.; Lanzalunga, O. Tertiary : Secondary : Primary C–H Bond Relative Reactivity in the One-Electron Oxidation of Alkylbenzenes. A Tool to Distinguish Electron Transfer from Hydrogen Atom Transfer Mechanisms. J. Chem. Soc., Perkin Trans. 2. 1996, 133–140.