I mainly make jewelry, and I only use saw cut. If I decide to make anything larger like armor, I might use machine cut so I wouldn't need to spend so much time on my closures.
I prefer saw cut. I like the way they close but I have seen some great armor made with some good machine cut rings too. I think it is a matter of preference and it is great that there are options for everyone.
I spoke to a girl today who makes chainmaille for horses. She said she can't use the machine cut as they get caught in the horse's mane and tail and then she has a really problem.
Neat Closures seem more of a breeze to accomplish with Saw Cut jump rings!! (IMO, when rings aren't neatly closed, there is a sense of professionalism that becomes greatly lost on the appearance of the jewelry piece!!)