The development of persona systems provides a possibility for end users to interact with different persona modalities. In a 54-participant randomized controlled experiment, we compare two persona interaction modalities, document and dialogue personas, both generated using AI approaches from survey data. Overall, dialogue personas appear to be perceived more favorably than document personas. However, document personas exhibit a wider range of perceptions, suggesting that experiences with document personas are more polarizing among users. The document personas had higher transparency and were perceived as more complete, but the task completion was perceived as more difficult, although the task success rate was higher. The dialogue personas were perceived as more usable, with a higher System Usability Scale score, and more enjoyable. Our findings provide critical insights into the increasingly important area of persona interaction modalities and the broad paradigm of human-persona interaction.