Nichrome gets heated more.

Heat produced: $H = I^2 R t$

Since both carry same $I$ and have same dimensions, $R \propto \rho$.

Resistivity of Nichrome $\approx 110 \times 10^{-8}$ $\Omega$m vs Copper $\approx 1.7 \times 10^{-8}$ $\Omega$m.

$$\rho_{Nichrome} \gg \rho_{Copper} \Rightarrow R_{Nichrome} \gg R_{Copper} \Rightarrow H_{Nichrome} \gg H_{Copper}$$