Ah, if only the pursuit of accuracy was as simple as buying the right tools and cases and bullets and getting the same OAL within a half thou and charges consistant to .000002 gr. Fact is, shooting skill and reloading skill and a good accurate load development process will have a far greater effect on targets than changing dies and tiny fractions of loaded dimensions or powder weight. The real question with dies isn't "what I like" but does higher cost guarantee any difference on target and that answer is an unqualified "NO". All dies are made within standard manufactoring tolerances and Lee's perform as well as any. And often a bit better.
I have found Redding and Forster Comp/BR full body length sleeve seaters consistantly do very good if not perfect work; they are tied for first place in my experience. On average, ALL other brands/types are tied for second place - and most dies are so good that second place is better than most shooters and rigs. In my measurements of well over fifty die sets I've found the output of individual dies differ as much between examples of the same brand as between brands.
Straighter ammo usually shoots straighter. The press used is largely irrelivant; dies are where ammo is made. Good seaters help but cases may be a bigger problem, lightly turned case necks can be helpful even in SAAMI chambers. I've found no sizer produces a higher average of straight case necks than Lee's collet neck dies; if someone gives me another bushing size die I'll take it but I won't buy another. I use home made "body sizers" of common FL dies with the necks reamed enough so the Lee collet die can then do it's thing; if you can't modify your own body dies, buy one. And, whatever neck sizer/expander you use, avoid any "neck tension" with a neck ID smaller than 1 to 1.5 thou under bullet diameter or you'll bend your nice straight necks when seating too fat bullets.