In speech language modeling, two architectures dominate the frontier: the Transformer and the Conformer. However, it remains unknown whether their comparable performance stems from convergent processing strategies or distinct architectural inductive biases. We introduce Architectural Fingerprinting, a probing framework that isolates the effect of architecture on representation, and apply it to a controlled suite of 24 pre-trained encoders (39M-3.3B parameters). Our analysis reveals divergent hierarchies: Conformers implement a "Categorize Early" strategy, resolving phoneme categories 29% earlier in depth and speaker gender by 16% depth. In contrast, Transformers "Integrate Late," deferring phoneme, accent, and duration encoding to deep layers (49-57%). These fingerprints suggest design heuristics: Conformers' front-loaded categorization may benefit low-latency streaming, while Transformers' deep integration may favor tasks requiring rich context and cross-utterance normalization.