Weigh the percentage the car will see extended street driving vs the time it spends at the drag strip, then factor in how much power the engine will make. If the intended usage weighs heavily towards the drag race side, and your combo makes less than 700 HP, I'd put a C4 in it for the reasons you have already mentioned. It is significantly smaller, and lighter than an AOD, and parts are significantly cheaper. If you are either making more power than that, or you want/need the gear reduction,. A 4r70W is much more power capable. But, it is a big assed transmission, it's accordingly heavy, and the larger internals require more power to spin. I built my own, and have built many C4's in the past. They are not the same.
My engine will probably make 350-400 RWHP, but it should make in the neighborhood of 550-600 RWTQ. In my case, the 4th gear was the needed item.
And yes,...if you do intend to build either an AOD, or a 4R70w, Silver fox is your goto.