= Solution
Derive both cases from $V=C_p(\Phi/M_{\rm Pl})^p$, using the positive-field branch. The <potential slow-roll parameter> and <second potential slow-roll parameter> are
$$
\epsilon_V=\frac{p^2M_{\rm Pl}^2}{2\Phi^2},\qquad
\eta_V=\frac{p(p-1)M_{\rm Pl}^2}{\Phi^2}.
$$
Taking the leading inflation-end estimate $\epsilon_V=1$, the remaining <number of e-folds> is
$$
N\simeq\frac1{M_{\rm Pl}^2}\int_{\Phi_e}^{\Phi_N}\frac{V}{V'}\,d\Phi
=\frac{\Phi_N^2-\Phi_e^2}{2pM_{\rm Pl}^2},\qquad
\frac{\Phi_N^2}{M_{\rm Pl}^2}=2pN+\frac{p^2}{2}.
$$
The corresponding <monomial-inflation curvature amplitude> and tilt are
$$
\mathcal P_{\mathcal R}(N)=\frac{C_p}{24\pi^2M_{\rm Pl}^4}
\left(2pN+\frac{p^2}{2}\right)^{p/2}\frac{4N+p}{p},\qquad
n_s-1=-\frac{2(p+2)}{4N+p}.
$$
In particular,
$$
\boxed{n_s^{(2)}=1-\frac4{2N+1}\simeq0.9669,\qquad
n_s^{(4)}=1-\frac3{N+1}\simeq0.9508\quad(N=60).}
$$
The quartic case is redder. Its small-$k$ matter envelope is $k^{0.9508}$ instead of $k^{0.9669}$; its high-$k$ envelope is $k^{-3.0492}\ln^2 k$ instead of $k^{-3.0331}\ln^2 k$. With the late cosmology fixed, the turnover and baryonic acoustic scale do not move. If the spectra are matched in amplitude at a pivot $k_*$, their ratio is approximately
$$
\boxed{\frac{P_m^{(4)}(k)}{P_m^{(2)}(k)}
\simeq\left(\frac{k}{k_*}\right)^{-0.0161}.}
$$
This gives more large-scale power and less small-scale power relative to the pivot, with about a $7\%$ relative tilt across two decades in wavenumber.
The quartic coefficient is not specified, so changing the power of the potential does not by itself specify the overall amplitude. If $C_2=V_0$ and the quartic coefficient is $C_4$, the formula above gives, at the same $N$,
$$
\boxed{\frac{\mathcal P_{\mathcal R}^{(4)}}{\mathcal P_{\mathcal R}^{(2)}}
=32\frac{C_4}{V_0}\frac{(N+1)^3}{(2N+1)^2}
\simeq496\frac{C_4}{V_0}\quad(N=60).}
$$
Consequently choosing the same dimensionful coefficient would give a very different normalization, whereas choosing $C_4/V_0\simeq1/496$ matches the pivot amplitude. These are different normalization choices, not a universal amplitude prediction from a quartic shape alone.
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