Neuromorphic vision systems based on spiking neural networks (SNNs) offer ultra-low-power perception for event-based and frame-based cameras, yet catastrophic forgetting remains a critical barrier to deployment in continually evolving environments. Existing continual learning methods, developed primarily for artificial neural networks, seldom jointly optimize accuracy and energy efficiency, with particularly limited exploration on event-based datasets. We propose an energy-aware spike budgeting framework for continual SNN learning that integrates experience replay, learnable leaky integrate-and-fire neuron parameters, and an adaptive spike scheduler to enforce dataset-specific energy constraints during training. Our approach exhibits modality-dependent behavior: on frame-based datasets (MNIST, CIFAR-10), spike budgeting acts as a sparsity-inducing regularizer, improving accuracy while reducing spike rates by up to 47\%; on event-based datasets (DVS-Gesture, N-MNIST, CIFAR-10-DVS), controlled budget relaxation enables accuracy gains up to 17.45 percentage points with minimal computational overhead. Across five benchmarks spanning both modalities, our method demonstrates consistent performance improvements while minimizing dynamic power consumption, advancing the practical viability of continual learning in neuromorphic vision systems.