Multi-touch attribution (MTA) aims to assess the effects of various touchpoints on conversions and refine advertising strategies. Recent developments in deep learning have shown substantial advantages in modeling complex user behaviors (i.e., touchpoint sequences) and capturing temporal dependencies in MTA tasks. However, it is unclear about the performance and improvement of deep learning-based MTA models reported in academia. In this study, we present a comparative study of nine MTA models on a synthetic and two public datasets in terms of conversion rate (CVR) prediction and advertising effectiveness. We observe that causal attribution models significantly enhance advertising attribution by addressing the confounding bias induced by user preferences; models with better attribution results perform better in CVR prediction and lead to more efficient advertising decisions (e.g., budget allocation).