Phenyl vs methyl cis/trans stability
The molecule contains conjugated system of double bonds, being essentially a substituted styrene. The phenyl cannot therefore freely rotate and its steric requirements are difficult to estimate just by hand-waving arguments.

Correct answer needs some quantitative argument, either e.g. heats of formation or calculation.

From the second, the energies come out using MMFF94 (using Avogadro):


Z: 177.6 kJ/mol
E: 175.6 kJ/mol 


Also, both the isomers rotated the styrene substantially from planarity. The difference in results is quite small and can easily change when using other method. According to the numbers I'd agree with your answer, Z is less stable. 

I would not consider this a valid question in test, the answer is not straightforward.