Research on cross-dialectal transfer from a standard to a non-standard dialect variety has typically focused on text data. However, dialects are primarily spoken, and non-standard spellings cause issues in text processing. We compare standard-to-dialect transfer in three settings: text models, speech models, and cascaded systems where speech first gets automatically transcribed and then further processed by a text model. We focus on German dialects in the context of written and spoken intent classification -- releasing the first dialectal audio intent classification dataset -- with supporting experiments on topic classification. The speech-only setup provides the best results on the dialect data while the text-only setup works best on the standard data. While the cascaded systems lag behind the text-only models for German, they perform relatively well on the dialectal data if the transcription system generates normalized, standard-like output.