I have a Lee press and system for .223/5.56 and it does fine. I get much better accuracy, tighter groups,  than with most factory ammo. I also have a set of Hornady dies for 9MM. The press isn't that much of an issue as the dies are, IMHO. But I have only been doing this for a year, so I am a green horn. 

If you get the powder measured accurately, case length, and the bullet runout, and bullet length correct for your firearm, you have won most of the battle.