Joint inference approaches such as Integer Linear Programming (ILP) and Markov Logic Networks (MLNs) have recently been successfully applied to many natural language processing (NLP) tasks, often outperforming their pipeline counterparts. However, MLNs are arguably much less popular among NLP researchers than ILP. While NLP researchers who desire to employ these joint inference frameworks do not necessarily have to understand their theoretical underpinnings, it is imperative that they understand which of them should be applied under what circumstances. With the goal of helping NLP researchers better understand the relative strengths and weaknesses of MLNs and ILP; we will compare them along different dimensions of interest, such as expressiveness, ease of use, scalability, and performance. To our knowledge, this is the first systematic comparison of ILP and MLNs on an NLP task.