Two different ways to deduct car purchase and related expenses

I read for section 179, if you buy a new or used SUV, as long as the GVWR is over 6000, you can write off up to $25,000 in the first year.  Then you can write off all gas and maintenance and toll/parking expenses in the following years.

 

I spoke to two different people and both gave me two different perspectives.  Both have a LLC where they manage investment properties.  

Person 1- buy car for her business under her personal name and writes off all car expenses.  Has a separate car strictly for personal.  Car insurance is in personal name and registration of car at dmv is under personal name.

 

Person 2- buy car for her business under her business name and writes off all car expenses.  Also has a separate car strictly for personal.  Car insurance is under business name and registration of car at dmv is also under business name.

 

So what’s the difference between the two in terms of eligible tax write offs?  Does the first one because it’s under personal name have certain limitations vs the second one? It almost seems like it’s one extra step to have everything under business with insurance and dmv so are there more tax benefits doing it the second way?