Idano,
"If the Lee Factory Crimp Die does a taper crimp how can it be any better then the Hornady or for that matter any other taper crimp die?"
1. I didn't think it was better, until I tried one in 9MM. I then found out the benefits of the Lee FCD. Benedict1 described how it worked real well, so I can add nothing worthwhile to his answer.
2. Another way it is better is it's included in the Lee Deluxe Die pistol sets, so when you buy the Deluxe die set, you get the whole sheebang for about $25.00, a darn good deal for four excellent dies.
"Also, does the Lee Factory Crimp Die clear the ejector wire on your Hornady AP or did you have to grind them down a little?"
I had to grind it down a little. I moved the ejector wire out of the way, inserted the Lee FCD in a LnL bushing, adjusted the die, then put the ejector wire back in place and marked how much of the die to grind. Took it over to the grinder and a couple minutes later, it fit the press and worked great. Didn't have to take much off and the Lee FCD die mouth is quite thick to start with.
The advantage is buying the 4 die sets that have everything you could want packaged in one nice set, including a shellholder if you're using a Lee Classic Cast turret, so it's an ideal buy for the turret. But is still a great buy for the LnL.
Regards,
Dave