Preferences are a pivotal component in practical reasoning, especially in tasks that involve decision-making over different options or courses of action that could be pursued. In this work, we focus on repairing and querying inconsistent knowledge bases in the form of graph databases, which involves finding a way to solve conflicts in the knowledge base and considering answers that are entailed from every possible repair, respectively. Without a priori domain knowledge, all possible repairs are equally preferred. Though that may be adequate for some settings, it seems reasonable to establish and exploit some form of preference order among the potential repairs. We study the problem of computing prioritized repairs over graph databases with data values, using a notion of consistency based on GXPath expressions as integrity constraints. We present several preference criteria based on the standard subset repair semantics, incorporating weights, multisets, and set-based priority levels. We show that it is possible to maintain the same computational complexity as in the case where no preference criterion is available for exploitation. Finally, we explore the complexity of consistent query answering in this setting and obtain tight lower and upper bounds for all the preference criteria introduced.