In this paper, the synchronization using proportional delay neural networks (PDNNs) as master-slave systems with heterogeneous dimensions is studied. By designing a reduced-order observer and a feedback controller, while choosing a Lyapunov-Krasovskii functional (LKF), a global asymptotic synchronization (GAS) criterion for the master-slave systems is obtained. Then, by optimizing the observer and the controller to be adaptive and selecting a Lyapunov functional (LF), a global exponential synchronization (GES) criterion for the master-slave systems is obtained. The proposed conditions can be conveniently represented and the validity of the proposed outcomes is confirmed via three numerical examples, and we provide an application scenario in image encryption. The primary contributions of this paper are twofold. First, we investigate the synchronization problem in master-slave systems with proportional time delays and heterogeneous dimensions, which differs from most existing studies, because many prior works on master-slave synchronization assume bounded delays and identical system dimensions between the master and slave. Second, we optimize the observer and the controller design to the adaptive observer and controller, which offers significant advantages in enhancing system adaptability, robustness, and performance in practical applications.