They both add Reply Value so they are equal in that department.
And I enjoy both very much so.
But....
I like achievements more because:
Every Single 360 Games has them.
I don't have to wait for my 360 to sync up with a server to see my achievements.
When I get an achievement I can quickly see what I got the Achievement for, no scrolling, just push button & view.
Achievements feel like a solid part of the system, as trophies seems like an added mod of some kind.
Trophies are still buggy, I Do Not own StarDust but yet it still shows on my trophy list as 0% Trophies ever sense i got the demo, and will not leave my trophy list..
PS4 Preordered - 06/11/2013 @09:30am
XBox One Preordered - 06/19/2013 @07:57pm
"I don't trust #XboxOne & #Kinect 2.0, it's always connected" as you tweet from your smartphone - irony 0_o