The first style is something akin to standard writing format in most types of prose - be it for school compositions, short stories or novels, even writing story outlines for movie and TV productions. And yes, you're correct to say that usually only one speaker per paragraph for clarity of who is speaking at each time, to avoid confusion.

I have never seen or heard about the second style, and I do agree with you that it's just [i]awkward[/i]. Not only does it break the reading flow, it's just not something you'd ever see in standard writing (mentioned in my paragraph above). I'd suggest you stick with the first one.

As I'm not a native English speaker, sometimes writing dialogue/character speeches is quite a challenge for me - in terms of making it sound natural as if they are spoken out loud, even if it's actually in written form. One way for me to minimize awkward speeches would be for me to read out loud what I have written in my dialogue, to physically feel how the speeches sound like, the rhythm of the spoken syllables, etc. Researching about slang is also helpful - even in English, there are difference between how an English (someone from UK) would speak and say certain things compared to an American.