I currently load on a Lee Loadmaster which on some days been a challenge, but I work through it. I'm contemplating buying a Dillon....
I've loaded for more than 50 years now, and I tried the Lee Loadmaster when my kids gave me one for Christmas 15 yrs ago...I'd idly suggested that I wanted to move on from my single stage press...a Herter's #3 from 1962. They bought me the Lee LM and I spent two miserable years trying to keep the damned primer assembly working right, not to mention the powder measure et al. That old Herters by the way routinely produced rifle ammuntion that had a runout of less than 0.003"...and on just about anybody's dies.
I boxed it up finally and bought a Dillon 550B, and it worked so well that I bought a 2nd one so's I didn't have to change out the primer assembly when switching from large to small primers. Both have loaded roughly 50,000 rounds of both pistol and rifle ammuntion, most of it match grade, including the 5.56mm stuff that I hauled to Camp Perry for several years.
If you're going to move up, to a good press, the Dillon is the way to go. One phone call, one, and they'll help you through any problem and replace any parts that go south on you. To date, I've had one return rod on the primer feed go bad...that's it and I had it in my hands two days after the phone call to them. Great people...
As to the press making a big difference in loading quality ammuniton, maybe....maybe....if it's grossly out of alignment it'll matter, or if you need bench rest precision probably, but for the rest, nope. Dies make little difference either other than quality of finish, or ease of use (the Dillon variety), but all are generally good. Lee included...I loaded all of my Camp Perry ammo with Lee dies and did fairly well for a 65 yo with fading eyes.
Do yourself a favor, and if you need a press that loads 200+ rounds of truly quality ammunition an hour, get the Dillon 550B or is it 550C now!
Best Regards, Rod