News media play a central role in shaping public perceptions of climate change, and whether coverage emphasizes threats or solutions affects audience engagement and policy support. We compare fine-tuned encoders and zero-shot prompting for classifying sentences from German-language climate news as threatoriented, solution-oriented, both, or neither, using two independent binary classifiers. We finetune three German encoders with context windows ranging from the target sentence alone to four preceding and four following sentences, and compare them with three open-weights generative models and the non-generative decision model Jev. All models are evaluated with article-grouped five-fold cross-validation on 440 manually coded Austrian newspaper articles. The best encoder, GBERT-large with the widest context, achieves weighted F1 scores of 0.805 (threat) and 0.802 (solution). The recently released MiMo-V2.6-Flash reaches 0.807 and 0.798 without task-specific training, placing both approaches on par, whereas earlier prompting models remain below the best encoder. Additional context improves all encoders consistently, by up to 4.8 F1 points. On the natural class distribution, MiMo-V2.6- Flash outperforms GBERT-large on threat classification, while GBERT-large retains a small advantage for solution classification. These results indicate that the gap between fine-tuned encoders and prompted language models has only recently been closed.