Understanding how learning algorithms shape the computational strategies that emerge in neural networks remains a fundamental challenge in machine intelligence. While network architectures receive extensive attention, the role of the learning paradigm itself in determining emergent dynamics remains largely unexplored. Here we demonstrate that reinforcement learning (RL) and supervised learning (SL) drive recurrent neural networks (RNNs) toward fundamentally different computational solutions when trained on identical decision-making tasks. Through systematic dynamical systems analysis, we reveal that RL spontaneously discovers hybrid attractor architectures, combining stable fixed-point attractors for decision maintenance with quasi-periodic attractors for flexible evidence integration. This contrasts sharply with SL, which converges almost exclusively to simpler fixed-point-only solutions. We further show that RL sculpts functionally balanced neural populations through a powerful form of implicit regularization -- a structural signature that enhances robustness and is conspicuously absent in the more heterogeneous solutions found by SL-trained networks. The prevalence of these complex dynamics in RL is controllably modulated by weight initialization and correlates strongly with performance gains, particularly as task complexity increases. Our results establish the learning algorithm as a primary determinant of emergent computation, revealing how reward-based optimization autonomously discovers sophisticated dynamical mechanisms that are less accessible to direct gradient-based optimization. These findings provide both mechanistic insights into neural computation and actionable principles for designing adaptive AI systems.