I know this is a very old topic, and maybe there's not a lot of interest, but a few months ago I was looking for information on the same topic, and after buying my XDs (I have the 4" model), I wanted to share my experience and opinions.
Most of what I found were comparisons of holding the guns in hand and range shooting, but not actually carrying, and there are a few things that I've not seen anyone mention
In the hand:
I don't have a lot to say here...both guns feel great in my hands. The 1911 fits my hand better than the XDs without the grip extension, but with it, there's little difference in feel to me aside from polymer vs aluminum/wood. I don't have a strong preference here, but if I had to choose, the 1911 would win.
Shooting:
For me, both guns shoot equally well. The 1911 is more comfortable/fun to shoot, so if I were going to hit the range for a few hours I'd choose it, but I have range guns that serve that purpose. I make a point to run 2 mags through my carry guns each time I go to the range just so I stay familiar with them and I know they still function, but I don't put 100's of rounds through at a time. I have to concentrate a bit more to shoot as well with the XDs as I do with the 1911, but the difference is only slight, and I'm still more that proficient enough with the XDs for defensive purposes. I like the trigger on the 1911 better for the range, but I actually prefer the trigger on the XDs for carry. Again, I don't have a large preference, but if I had to choose, the 1911 would win again.
Carry:
I've carried a Springfield RO Compact .45 model 1911 for around 2 years. I love the gun...it shoots great, has a beautiful trigger, is pretty lightweight for a 1911, is more accurate than an Officer's model, and is an all around beautiful firearm. But for me, carrying a 1911 isn't without it's drawbacks. Although fairly lightweight for a 1911 (there are some that are a few oz's lighter, but not much), it's still on the heavy side for a carry gun, but that doesn't really bother me, because I typically enjoy the increased weight when shooting larger calibers. I don't love carrying with a thumb safety. Not only do I have to remember to disengage it if I ever have to use the firearm in a defensive situation, but it does make the gun wider, even if only at that one point. I usually carry with the thumb safety off, as you still have to activate the grip safety and trigger before it'll fire, but I just don't love it being there. The RO Compact has a very nice match trigger...probably the best trigger of any handgun I own, but I don't love it for carry. I figure in a high stress situation, that crisp 3-ish lb trigger with almost 0 travel could easily be stress fired. However, my biggest problem with carrying a 1911 is the beavertail. I'm not a...skinny guy, and my job requires me to be seated for about half of the work day. I carry in a Sticky Holster, which allows me to carry in whatever position I want, but there is nothing that I can do to keep the beavertail from digging into me and becoming uncomfortable after a few hours of sitting. When I'm standing it's fine, but in the car and at work, I can constantly feel it digging into my side. It's not bad enough to prevent me from carrying, but it's bad enough to be annoying. Enter the XDs. The XDs does everything for me that the 1911 does in a carry sense. It's chambered in 45 ACP, it's slim, it's accurate, it's reliable, and it has a good sight radius for a carry gun. It's about 4oz lighter, but that isn't a big deal to me, although I do notice the difference. However, it does 2 things for me that the 1911 cannot. First, I can choose to carry without the extended magazine. This is important for me when it's really hot out, because I tend to wear thinner tshirts, and my 1911 always printed in those, though not badly. My XDs however, doesn't print at all unless I pull the shirt tight around it if carrying with the flush magazine. More importantly, I don't have the issues with the thumb safety or trigger that I do with the 1911. There is no thumb safety, and the trigger is mushier, though still nice and crisp once you get through the "take up." Again, not as desirable at the range, but more desirable for carry. Most of all, I don't have that huge beavertail to worry about digging into my side, making the XDs far more comfortable to carry over the course of the day. The 1911 does have a round-count advantage, but if I can't do the job with 6-7 rounds, the additional 1-2 that the 1911 can handle probably wouldn't have made a difference. While I won't hesitate to carry my 1911, the XDs is the clear winner in this category for me.
Other thoughts:
Versatility:
One thing that I've not noticed anyone mention is versatility. While this specific example isn't really a big deal to me, and probably won't be to most people, the XDs does come with a rail from the factory. To my knowledge, there are no small-frame (officer's size) 1911's that come with a rail. The XDs, whether 3.3" or 4" does. This allows you to attach a flashlight and stick the gun on your nightstand, or a laser for the range (to be fair, you can get laser grips for the 1911). The XDs wins in versatility, if only by a small margin.
Customization:
If customizing is your thing, the 1911 is the clear winner. There are far more options to customize your 1911 than your XDs.
Reliability:
The XDs didn't have a great launch. There was at least 1 recall that I'm aware of and it had a few issues. However, those have since been worked out, and were never an issue in the .45 model if my understanding is correct. Small 1911's don't have the greatest reputation either, especially 3" Officer's models. I think that has improved greatly over the years, but I know several people who've had enough bad experiences that they avoid them. That being said, my personal experience with both is great, so I don't have a clear winner. Both of mine have been 100% reliable, as was my Kimber Ultra Carry II (I traded that for the RO Compact when I got it).
Overall, I prefer my 1911 for pretty much everything except for carrying, where the XDs wins out for comfort. I'm keeping the RO Compact because it is probably my favorite pistol, but the XDs is my new go-to for EDC.