We know from the segment on Narrators that writing in the First Person has the hero as his own narrator. In the third person the narrator, while they may be a character, is a separate entity in your head as you read.
I have a preference for this voice as a writer of gay teenage romance. It means I can create the 'I have no idea if my adoration will be reciprocated' tension as something that is real to me. Why? Because that is what I experienced as a teenager and that is what I am writing.
So, for me, the story flows better because I can live it as myself
Despite my having a preference away from Third Person, I can write in it and have done so. One of my Nice Try! Mini-series is written in Third. It was a conscious choice to move to it in a series that was written first by one of our heroes, then by the other, and finally by both/neither.
I wonder about stories that have subheadings to introduce a character and then proceed in his voice until the next subheading to introduce another character. I find them hard to read because they place an obstacle in my path - the need to remember who is talking. The question I have for you as an author is whether you want to place obstacles in your readers' path.
I experimented with this slightly differently in Holiday in the Sun. I realised it was hard to work out who was speaking, so I went for an approach managed by style. Even so I am not sure it works well. The tale was an experiment in telling the same first person tale almost simultaneously, so it was a literary stratagem.
You need to reach a conclusion about the Switcheroo. My preference for the majority of tales is for those that need different people telling the tale to be written in the Third Person, and to choose the correct type of Narrator.