Its normal that the car jolts a bit when coming to a stop. Its not as serious as it may seem. Just an operational thing. If it is an extremely powerful jolt, you may want to take it to a shop.
The AX4N and AX4S only select gears in which the car shifts in to, they do not determine power. It seems to me you may have had a Vulcan/AX4S and a Duratec/AX4N.
(Edit: Maybe someone can enlighten me on Gear ratios. I believe both the AX4N and AX4S had a 3.77 ratio, but im not 100% sure.)
its a small nudge, and it dont do it all the time. i was just a little worried because my ax4n didnt do that and my moms ax4n didnt do that.
i know ax4s's have some problems and i tried to to get one but for $2150 @ 97k it was a good deal.
when i dropped the pan and changed the filter and fluid the metal magnet had barley anything on it, so it looks like the tranny is in good shape.