I've loaded much ammo with Lee dies. They are what I started out with when money was more tight than now. There is absolutely no doubt in my mind that Lee dies can and will load accurate ammo. The two biggest problems with Lee dies IMO:
1) Less polished on the inside, will sometimes scratch brass or "stick"
2) The bullet seaters, in certain cartridges, not all, will sometimes either not seat bullets as uniformly and/or, will deform the tips
Lee collet dies work pretty well, and the Lee factory crimp dies are great.....
That said, Reddings are my favorite dies now. Hornadys my least favorite......