My sub is a JL Audio 10W3 V2 powered by a JL Audio 250/1 V1 amp in my own custom made box and I am very impressed with it.
The A1200 is 120 W RMS x 1 @ 4 ohm or 200 W RMS x 1 @ 2 ohm at 12.5 V.
Using a 10" Jl W3v3 you have a choice of a 2 ohm version or a 4 ohm version so if you get the 4 ohm version and supply it with 12.5V you are 130 W RMS down on the same set up with the 250/1 which will make a difference (this difference will be less at 2 ohms and a higher voltage).
The JL Audio 250/1 is 250 W RMS @ 1.5 ohm-4 ohm (11V-14.5V) basically the amp will supply 250RMS within those figures so the speaker ohms and the power input voltage do not make a difference to the RMS.
The 250/1 is also a class D amp which is more efficient but does produce higher distortion than AB design of the A1200, however you will not hear any distortion due to the low pass filter.
The low pass filter on the 250/1 does have the ability to set the octave slope to 12 or 24 dB (only 12 dB is available on the A1200) which can fine tune a system better. JL recommend 24 dB octave slope for W3 range of subs although it is not set in stone I tend to agree on my set up.
Also the 250/1 has a low frequency boost built in so you can boost the base in a range of 0-15 dB the A1200 is either 0 or 6dB unless you buy the remote base port lead.
So in summary you can fine tune a system better with the 250/1 and with a 4 ohm speaker it will be a lot more powerful (the optimum power for the 10" Jl W3v3 is 300 w RMS, minimum is about 100 w RMS).
In the real world with a 2 ohm 10 W3v3 the A1200 will sound great with a 4 ohm not as good.
The 250/1 is nearer the optimum power for the 10 W3v3 which is probably the most important part.
Hope that helps
Craig