Given the relative forces (D. H. Hill's division vs as most of the AOTP), South Mountain certainly should have been a massive Union success. As it was, it proved an effective delaying action. Then the following day the AOTP didn't act with the haste they should have.
DH Hill's division against 9th and 1st Corps; they couldn't fit the rest of the force down the road to get involved, and indeed it takes hours to squeeze 9th and 1st Corps up to the fighting front in the first place. Later on Longstreet joins in.
In terms of pre-straggle PFD (which is fair because most of the straggling takes place after this point):
DH Hill is about 10,000.
9th Corps and 1st Corps combined are about 30,000 PFD (which is the available strength once the whole of both corps have had time to arrive and deploy).
Longstreet's division(s) when they arrive are about 14,000.
3:1 odds defending a mountain pass is not all that bad a situation (it's certainly better than doing so in an open plain) though this situation was never actually going on at any specific time to the best of my understanding (i.e. the whole of 1st and 9th Corps hadn't had time to arrive before DR Jones, Hood and Evans start to turn up and join in). The CEV numbers for it are around .64 (including Cramptons Gap) which is pretty good on the attack against Lee especially as this doesn't adjust for the mountain pass (which prevents the force with superior numbers from employing that superiority, at least once the force with smaller numbers has enough that they can form a complete block across the gap).
The next day everyone gets moving in a timely fashion except 9th Corps, which can probably be laid on Cox.
Cox delayed considerably after getting the order (in his write up of the situation after the fact he claimed that he didn't get the order to move until nearly noon), so when Sykes arrived he pushed through first. It is not clear whether Burnside or Cox erred, but the formal written order to Burnside was to "advance with your whole corps upon boonsborough" and was dated 8AM; if Cox says he didn't get the order until nearly noon, either Burnside erred in not passing it on or Cox erred in not following it.
The other column to the north sees Richardson passed through first as a fresh division, then 1st Corps follows, and Sykes (first through to the south) and Richardson (first through to the north) are at the Antietam by the late afternoon - an advance of 7-8 miles from the positions at the end of the 14th, and more importantly an advance to the point where they have to stop and "go firm" to await reinforcements, as Longstreet + DH Hill combined outnumber Sykes + Richardson considerably.
On a related note: I would very much like to see someone write a book that covers the AOTP and ANV in depth from Sept 21 to Nov 5, 1862. In other words, from when the ANV was safely across the Potomac until McClellan was relieved of duty. Something in the vein of Jeffrey William Hunt's Meade and Lee After Gettysburg: From Falling Waters to Culpeper Court House, July 1863. I don't think there's any in-depth coverage of this period, especially not with maps.
I've done a look at it, if that would help? Starts here:
https://civilwartalk.com/threads/putting-all-the-mcclellan-stuff-in-one-place.182980/post-2387484
And goes through the rest of the thread until I start doing the summing-up.