I can't think of many advantages, but I can't think of any disadvantages either. Personally, I find them good. You just have to change your mindset if coming from a Boeing.
If the AT is in, you just treat them as the thrust limit selection switch and let the FMGS do it's work. And having the switch move in the correct sense rather than having to use the rather confusing THR switch on the MCP of the Boeing is a big plus. If you want to use man thrust, then they work just as any other aircraft. The fact they don't move with the power setting with the AT in is fairly inconsequntial and I have found in over 3500 hours of bus flying that I haven't missed that.
One small advantage I can think of is that on the take off roll, you get the thrust you ask for and if not set correctly, you get ample warning. Remembering the Bus takes off in manual thrust, AT is only armed until thrust reduction altitude when Climb is selected. Personally, I was never that happy with the way Boeing managed the thrust on the take off roll. You could manage it yourself by overriding the clutches, but it was one more thing to worry about at a critical part of the flight. Have a look at the thread regarding the Air France RTO at Lagos in Rumours and News to see how it can go wrong.