Traditional document similarity measures provide a coarse-grained distinction between similar and dissimilar documents. Typically, they do not consider in what aspects two documents are similar. This limits the granularity of applications like recommender systems that rely on document similarity. In this paper, we extend similarity with aspect information by performing a pairwise document classification task. We evaluate our aspect-based document similarity approach for research papers. Paper citations indicate the aspect-based similarity, i.e., the title of a section in which a citation occurs acts as a label for the pair of citing and cited paper. We apply a series of Transformer models such as RoBERTa, ELECTRA, XLNet, and BERT variations and compare them to an LSTM baseline. We perform our experiments on two newly constructed datasets of 172,073 research paper pairs from the ACL Anthology and CORD-19 corpus. According to our results, SciBERT is the best performing system with F1-scores of up to 0.83. A qualitative analysis validates our quantitative results and indicates that aspect-based document similarity indeed leads to more fine-grained recommendations.