Answer
Since $P=\frac{V^{2}}{R}$, the bulb of higher power has a smaller resistance. So, higher power means thicker wire if the length is the same , since resistance is smaller. So the wire in the 60W-bulb would be thicker.
Work Step by Step
Since $P=\frac{V^{2}}{R}$, the bulb of higher power has a smaller resistance. So, higher power means thicker wire if the length is the same , since resistance is smaller. So the wire in the 60W-bulb would be thicker.