Personally I think that Antietam would be rightfully credited with being a turning point of the war. Antietam gets much less attention then Gettysburg. Over here the huge majority of people will have never even heard of the battle of Antietam / Sharpsburg and I think even in the US the battle is not nearly as well known. The American spirit of prefering clear winners and loosers may contribute to the lesser degree of attention given to a battle which was kind of a tactical draw and even for the strategic victory more of a missed chance to win the war there and then. It is the political consequences that make the battle of Antietam arguably more important than the three days of Gettysburg.
Prior to the proclamation of emancipation there was a chance that France and Great Britain might have intervened into the war. It is often overlooked that for Great Britain the imports of grain from the northern states were almost as important as the cotton imports from the southern states. However, with a deceicive southern victory at Antietam Great Britain (and France in its wake) may have seen the chance for the war to end within a few months at most after their intervention. Long story short, I think a different outcome of the battle of Antietam might have had a really tremendous effect on the outcome of the war. However, it should also be noted that if Great Britain and France had not intervened in the aftermath of a southern victory at Antietam, there would have been very little gain for the south. With their army being likely to be cut down to something between 30 000 and 40 000 men even in case of a stunning victory it is very questionable whether they could have taken the heavily fortified capital where the entire Corps of Franz Siegel had been held in reserve during the battle (much to the disappointment of German newspaper reporters at the time as I might add
) and to which large parts of the remains of the Army of the Potomac would have withdrawn. Any attempts of Lee to then exploit the victory by marching further north (with men who were described as starving by witnesses) rather than against Washington would have opened up all of Virginia to the federal forces who would cut any lines of supply and communication between Lee and Virginia. So the question of foreign intervention really appears to be the decicive one concerning Antietam.
On a side note, the battle also had photoraphers, Alexander Gardener and Matthew Brady, on the battlefield right after the battle for the first time in history, shocking the newspaper readers with pictures of the grim realities of war rather than fancy hero pictures in the days after the battle.
This june I'll hold a presentation on the battle of Antietam and am looking very much forward to it.
With Gettysburg it is a bit more complex. The farthest point on Cemetary Ridge to which soldiers from North Carolina (not from Pickett's all Virginian Division) got during the attack of the third day has often been labeled the High Water Mark of the Confederacy. I think that if the Confederacy still did have any chances of winning the war by that time they were a lot lower than at Antietam. The chance of the deceicive factor of foreign intervention hat pretty much ceased to be a possibility of any kind since the proclamation of emancipation was in place. An economic / military victory for the south was pretty much impossible with the huge northern superiority in terms of industry and population. The preceeding years as well as the northern blockade had drained the south notably already. Even if we assume a most stunning success of Pickett's charge and a federal retreat to Washington (and its fortifications) it would have still been no more than about 50 000 confederates pitted against some 60 000 federals in fortifications (and those numbers assume very limited southern and very high federal losses and do not even count the numbers of reserve troops in the Washington era). And what happens if even numerically superior attackers attack fortifications head on was most gruesomely shown in many battles of 1864 such as Spotsylvania and Cold Harbor. So even a southern victory at Gettysburg would not have meant the necessary capture of Washington D.C. (perhaps there would have been a greater chance for that if Lee had followed Longstreets advise to march between the Army of the Potomac and Washington and let the federals attack fortified rebels rather than the other way round).
With no chance for foreign intervention and no chance of overcomming the north by military success and industrial capacity alone the only remaining chance for the south to win the war would have been for people in the north to declare themselves defeated shocked by southern victories and in spite of the northern economic, industrial and numeral superiority of which people were well aware back then.
And here I think is the big question. Would people in the north just accept secession of the south and accept defeat? Personally I think that this question is one loaded with myth in public perception. Comparing "Johnny Reb" and "Billy Yank" there is little doubt that many Americans (perhaps even a majority) find "Johnny Reb" a lot more inspiring. The Rebels are attributed with an aura and a "coolness factor" which by comparison "Billy Yank" is rarely granted. One of the effects is that in modern day reenactments the numeral ratio between Rebs and Feds is often switched about with the Southerners outnumbering the Northerners by a multitute. Often members of Southern reenactment groups need to volunteer to act as federals to avoid the later from being ridiculously and unhistorically outnumbered. In public perception and representation heavily based on the "Lost Cause myth" southerners are presented as the decent, heroic, sacrificially, soldiers fighting for principles (and slavery is often denied by many to deserve any mention in this). Billy yank on the other hand is often depicted as the overequipped, well fed, aggressor making up for military incompetence by sheer numbers and with very little of that "aura" bestowed upon the southerners. This I think is a very unfair depiction of the northern soldiers. The many federal defeats (in particular the one in the first battle of Bull Run / Mannassas) contributed to the image and while ineffective generals rather than cowardice on the part of the soldiers (calling the blue coats sent row after row against the walls at Morris Hights near Fredericksburg cowards goes too far for most of the even most vehement neo-confeds) are rightfully often given the brunt of the blame for federal defeats the northern soldiers are often just not given nearly the recognition that the southern soldiers got and the same goes for the civilian population of both countries. Now make no mistake, the southern soldiers often did suffer more from lack of supply than the northerners did, but when faced with these problems (and with southerners suffering from incompetent generals) Billy Yank did hardly any worse than Johnny Reb. The siege of Chatanooga and the battle of Missionary Ridge are the best examples for this.
The people home in the north too may have a much stronger will to see the Union maintained than they are often given credited for. If we assume the rather unlikely scenario of the south capturing Washington after a victory at Gettysburg in the summer of 1863 I am not certain if this would have lead to the expected collapse of the northern will to fight. I do not totally exclude the possibility that it may have (and the New York draft riots shortly after Gettysburg stand examplary for a degree of discontent especially motivated by racism and the perception of a poor class many of whom were imigrants to fight a "rich mans' war on behalf of the *insert n word here*"), but I would not put those chances too high. The occupation of Washington D.C. by the Brits in 1814 had not caused for the country to collapse and while I agree that the situation of the civil war in 1863 was one completely different thing Washington D.C. still remained more symbolic (admittedly a very powerful symbol) than of any real strategic importance. The readiness of many northerners to continue in 1864, vote for Lincoln and against McClellan (who by the way also never ever said anything to the effect that he would accept the breaking of the union), are examples for the readiness of people in the north to see this war through and not accept anything but reunion (though admittedly there were significant numbers of people who would have been more than ready to accept reunion and a continuation of slavery).
To sum it up very shortly, I believe that a different outcome of the battle of Antietam could have altered the outcome of the war
if it had resulted in the intervention of England and France on behalf of the confederacy. On the other hand I believe that the degree to which a southern victory at Gettysburg might have altered the general outcome of the war is often overestimated. I do not believe for the significance of the battle of Gettysburg to be as overestimated as the battle of Waterloo (had Napoleon won at Waterloo I believe it would have prolonged his reign but for only a few weeks or months at most), but I still think it was not as much of a turning point as Antietam was and that the attention Gettysburg gets is based more on the numbers (it being the largest battle in terms of men fallen there) and location (it being the northernmost major battle of the war) than real potential to completely alter the outcome of the war.
As for the perception of Southern vs. Northern soldiers in the civil war I would like to conclude this post with a response which George Edward Pickett is supposed to have given when asked later why the charge at Gettysburg that bears his name failed:
"I've always thought the Yankees had something to do with it."
