I did also take note of how both movies play with different genres and even combine two completely different feeling stories within themselves, but I think the effect is really very different for each movie. In Out of Sight I think it drew less attention to itself, the romantic comedy aspect was played into the story pretty well. There's that moment in the trunk scene where they acknowledge that the plotline is going to be a little silly and unrealistic, but it's a good move because then you kinda just go along with it.
In My Own Private Idaho, it's much more noticeable. Here it really felt like we were intercutting between two different movies, it didn't form a cohesive experience as well as Out of Sight did. I primarily attribute this to the language. I loved the Shakespearean stuff, but it is so abrupt when it cuts in and out of it that you can't help but notice it. I'm not sure how well the rest of the movie would have worked if they had worked more of that type of language throughout, but I was definitely thinking about it more than I would have liked. Still, it's excusable because the whole movie feels like a mishmash of scenes, and it's played in such a surreal / absurd way that it's not too out of place.