Just for the sake of numbers, let's assume a 4" spinal column. A hit would be the diameter of the spine plus twice the bullet diameter. A .45 cal adds almost an inch of dia, vs a 6.5 which would only add ~ 1/2 inch (ignoring wound channel width). The larger caliber has a greater chance of wrecking something vital, by odds alone. IMHO, of course.
Not quite. Assuming your target was 4" wide, and merely touching it would be enough, the bullet has to have its centreline within half a diameter of the edge, either side. Thus in theory at least the .45 could be centred a bit over .22" from the edge, while the 6.5 would have to be within about .13", giving you 0.09" extra leeway on either side.
Of course in practice it doesn't quite work that way, as I guess you know. Among other things it is not enough to make a glancing hit. You really need to damage the spinal cord itself, or a nerve junction to the spinal cord. That may be by the bullet driving through it, or by bone fragments driving through it, or by vertebrae being displaced enough to cut the connection (though that might only have a temporary effect, if the spinal cord isn't actually severed). A wider bullet might give you a tiny edge, just by virtue of its greater diameter, but it is a tiny difference really. More significant on bigger animals might be greater momentum, to drive through muscle and bones to get there. Equally, a bullet might expand, provided it still can penetrate deeply enough, so bullet construction comes into play too, and a fast expanding bullet (as long as it doesn't fly to bits and fail to get there) might scatter bone fragments through the spinal cord or a nearby nerve junction on its way past - I've certainly seen that.
