What determines whether a molecular property prediction model organizes its representations so that geometric and compositional information can be cleanly separated? We introduce Compositional Probe Decomposition (CPD), which linearly projects out composition signal and measures how much geometric information remains accessible to a Ridge probe. We validate CPD with four independent checks, including a structural isomer benchmark where compositional projections score at chance while geometric residuals reach 94.6\% pairwise classification accuracy. Across ten models from five architectural families on QM9, we find a \emph{linear accessibility gradient}: models differ by $6.6\times$ in geometric information accessible after composition removal ($R^2_{\mathrm{geom}}$ from 0.081 to 0.533 for HOMO-LUMO gap). Three factors explain this gradient. Task alignment dominates: models trained on HOMO-LUMO gap ($R^2_{\mathrm{geom}}$ 0.44--0.53) outscore energy-trained models by $\sim$0.25 $R^2$ regardless of architecture. Within-architecture ablations on two independent architectures confirm this: PaiNN drops from 0.53 to 0.31 when retrained on energy, and MACE drops from 0.44 to 0.08. Data diversity partially compensates for misaligned objectives, with MACE pretrained on MPTraj (0.36) outperforming QM9-only energy models. Inside MACE's representations, information routes by symmetry type: $L{=}1$ (vector) channels preferentially encode dipole moment ($R^2 = 0.59$ vs.\ 0.38 in $L{=}0$), while $L{=}0$ (scalar) channels encode HOMO-LUMO gap ($R^2 = 0.76$ vs.\ 0.34 in $L{=}1$). This pattern is absent in ViSNet. We also show that nonlinear probes produce misleading results on residualized representations, recovering $R^2 = 0.68$--$0.95$ on a purely compositional target, and recommend linear probes for this setting.