Decision trees remain appealing for high-stakes tabular tasks thanks to readable rules and auditability, yet―even with CART, optimal trees, and gradient-trained variants―they often lag behind black-box learners. We close this gap with Multi-Branch Neural Decision Trees with Adaptive Pruning (MBNDT), a fully differentiable tree that jointly learns feature selection, multiway thresholds, and structure via gradient descent. To prevent routing collapse and promote calibrated partitions, we introduce light regularizers on branch load (traffic balance), threshold spacing/anchors, and minimum branch coverage. Across diverse tabular benchmarks, MBNDT matches or surpasses classical decision-tree methods and recent gradient-trained trees. Our results show that a carefully crafted differentiable design―ordered multi-branch thresholds, single-path straight-through routing, and mask-driven adaptive pruning with mild regularization―recovers much of black-box accuracy while preserving symbolic interpretability.