Get the Dillon. If you only plan on reloading pistol calibers, get the Square Deal, otherwise get the 550. I have both.
The Square Deal uses specialized dies (available from Dillon), but it auto indexes (rotates) with each pull of the handle, the 550 doesn't, you have to index it by hand, but it's a natural motion done with the left thumb. You can get all sorts of add on "gizmo's" to increase the speed of reloading for the Dillons. I haven't used mine in a while (twenty years), since I have been shooting military ammo, which was so cheap, it didn't pay to reload, and my hunting ammo, is done on a single stage press, because, I only use one or two rounds per season. Because of the current ammo situation, I called Dillon up and asked them if they could clean and tune it up, the answer was yes (for a minimal fee). Waiting to get it back, then I plan on reloading 223 on the 550.
Dillons warranty is just great, it's a: "you break it they fix it" type warranty. Sometimes the parts are free, customer support is also great. I'm not knocking the Hornady, as I never had one, just very happy with my Dillon presses.