IMHO, the main advantage I see from using a mandrel, at least for me, is that the mandrel step seems to turn
good ammo that's already
decently consistent, into
great ammo that's
super consistent... The difference is pretty small, but there is a difference, and since adding the extra mandrel step to my process is fairly painless (it's easier than just about every other step), I continue to do it. The mandrel step does seem to reliably and repeatedly lower my SDs, but it's not going to make up for anything else or really do shit for guys who haven't got their process already mostly figured out.
I too have done a couple/few different non-scientific "this vs that" comparisons like
@morganlamprecht mentioned... and like him, in general, the main thing I learned is that a ~$20 Lee sizing die is just as good as any other sizing die (sorry if anyone reading this has fallen for any of the $300-600 sizing die grifts out there, it's all BS lol). But, for me, the stuff that had seen a mandrel was always better, again, the difference wasn't huge, but there was a difference.
All that said... I mentioned it before, but I probably noticed the biggest difference once I realized that I should wait on running the mandrel through the brass until after I'd already lubed, sized, and then tumbled all the sizing lube off... the mandrel really does seem to "fix up" the case mouths/necks post-tumble to where it's noticeably better than hitting the mandrel before I'd tumbled all the lube off (hear me now believe me later, try it).
So, arguably, the positive effects I've seen with using a mandrel might have more to do with fixing up my mouths/necks post-tumble versus anything else...