Online clickbait continues to plague social-media platforms, where sensational captions lure users into low-value or misleading content. While prior work has explored individual modeling choices, i.e., sequential encoders, graph-based representations, and simple fusion strategies, no study has systematically compared these design dimensions in the clickbait domain. We address this gap by conducting the first comprehensive analysis of three core axes: (1) how to organize the model streams (treating caption and hashtags jointly vs. separately), (2) how to learn text representations (sequential vs. graph-based), and (3) how to fuse these modalities (concatenation vs. co-attention). Leveraging a large, manually labeled Instagram dataset of short captions paired with hashtags, we implement every combination of these axes to isolate their individual and joint impacts on detection performance. Our experiments reveal clear trends: processing caption and hashtags in parallel streams preserves their distinct semantic patterns and consistently outperforms unified processing; graph-based embeddings capture long-range and corpus-wide co-occurrence structures that sequential models alone miss; and a co-attention fusion mechanism aligns caption and hashtag signals, uncovering subtle mismatches characteristic of clickbait.