Optical Music Recognition (OMR) and Automatic Music Transcription (AMT) stand for the research fields that devise methods to transcribe music sources---documents or audio signals, respectively---into a structured digital format. Historically, they have followed different approaches to achieve the same goal. However, their recent definition in terms of sequence labeling tasks gathers them under a common formulation framework. Under this premise, one may wonder if there exist any synergies between the two fields that could be exploited to improve the individual recognition rates in their respective domains. In this work, we aim to further explore this question from a Transfer Learning (TL) point of view in the context of neural end-to-end recognition models. More precisely, we consider a music transcription system, trained on either image or audio data, and adapt its performance to the unseen domain during the training phase using different TL schemes. Results show that knowledge transfer slightly boosts model performance with sufficient available data, but it is not properly leveraged when the latter condition is not met. This opens up a new promising, yet challenging, research path towards building an effective bridge between two solutions of the same problem.