The adoption of vision-language models (VLMs) for wireless network management is accelerating, yet no systematic understanding exists of where these large foundation models outperform lightweight convolutional neural networks (CNNs) for spectrum-related tasks. This paper presents the first diagnostic comparison of VLMs and CNNs for spectrum heatmap understanding in non-terrestrial network and terrestrial network (NTN-TN) cooperative systems. We introduce SpectrumQA, a benchmark comprising 108K visual question-answer pairs across four granularity levels: scene classification (L1), regional reasoning (L2), spatial localization (L3), and semantic reasoning (L4). Our experiments on three NTN-TN scenarios with a frozen Qwen2-VL-7B and a trained ResNet-18 reveal a clear taskdependent complementarity: CNN achieves 72.9% accuracy at severity classification (L1) and 0.552 IoU at spatial localization (L3), while VLM uniquely enables semantic reasoning (L4) with F1=0.576 using only three in-context examples-a capability fundamentally absent in CNN architectures. Chain-of-thought (CoT) prompting further improves VLM reasoning by 12.6% (F1: 0.209->0.233) while having zero effect on spatial tasks, confirming that the complementarity is rooted in architectural differences rather than prompting limitations. A deterministic task-type router that delegates supervised tasks to CNN and reasoning tasks to VLM achieves a composite score of 0.616, a 39.1% improvement over CNN alone. We further show that VLM representations exhibit stronger cross-scenario robustness, with smaller performance degradation in 5 out of 6 transfer directions. These findings provide actionable guidelines: deploy CNNs for spatial localization and VLMs for semantic spectrum reasoning, rather than treating them as substitutes.