I think there's a difference between all the different methods, but the difference may be smaller than one might think.
In my mind, the main popular methods are: squashing the necks too much and then pulling up on the shoulder/necks with an expander ball (traditional FL die w/ expander ball), versus just squashing the neck as little as is needed and doing nothing else (FL bushing die), versus squashing the necks a tiny bit too much on purpose and then pushing through the necks going down so the shoulder has the most rigidity to hold its shape (honed-FL or bushing die followed by a mandrel die). More and more I'm starting to think that if one anneals every firing, one might be able to just pick one of the second two...
Brass is relatively malleable, and we're stuffing it in a steel chamber and then causing an explosion that yields thousands of pounds of pressure which blows it out to custom-fit the chamber it was just blown up in... so I'm not confident the minute differences matter as much as some might think. Arguably, a little more or less neck tension when the round was made means nothing when faced with all that pressure once the firing pin drops. However, I think how the round initially fits in the chamber is important, I want the same fit every time if I can before the big boom, so I prefer the methods that distort the shoulder the least (no expander ball).
For me, I think using the mandrel helps me make each round come out as near-identical to the next as I can, so I'll continue to use it, but I don't think it's the huge deal I once did.