Canopy height models (CHMs) are raster maps representing normalized tree canopy height above ground and are often used as co-products for estimating carbon storage, forest degradation, and biodiversity at regional to global scales. While airborne LiDAR delivers the most accurate canopy height (CH) measurements, its high cost and limited temporal coverage motivate the use of space-borne (multispectral) imagery combined with machine learning. In this study, we compare two distinct deep-learning approaches for continental-scale CHM estimation from 3 m PlanetScope imagery: (1) a CNN-based regression model (DeepLabv3+), and (2) a monocular depth-estimation model (Depth Anything V2) based on a foundation model. We train/fine-tune both models on a curated dataset of 16,973 pairs of airborne point cloud-derived CHMs and PlanetScope imagery of Australia using a stratified sampling scheme to ensure balanced representation of vegetation structural classes. We then evaluate their generalizability on independent validation sets across Australia, across different heights, and under limited-data scenarios. Through extensive quantitative and qualitative analysis, we show that the DeepLab-based regression model outperforms Depth Anything across all evaluation metrics, partly because it can incorporate additional spectral channels. DeepLab also learns more effectively from less data. On our dataset, the conventional CNN-based regression model performs better than the fine-tuned foundation model.