Ok so I've had some more time to drive the DS and compare to my X3 a bit and answer your question better.
For reference, the X3 is a 2013 28i.
Feel. The DS feels more like a truck - Heavier, more solid, larger and higher off the ground...even though it's not really bigger (haven't measured, but the DS seems pretty close to the X3 parked side by side). The X3 is more car like and nimble, but lacks in the solidity department. I prefer the overall feel of the DS, but they both have advantages.
Drive wise, both have nice acceleration and improve performance when the sport modes are engaged. I'm getting used to pushing the DS faster around corners and it handles nicely. While mostly a non-issue, the turbo lag rears it's head occasionally. For me, it seems to be when the car transitions from decelerating to a sudden acceleration (like coming to to a red light that turns green before you fully slow down). Mostly, I'm just learning to work with the car and understand how it responds. By adjusting my driving style a bit, I find it to be a very enjoyable experience. The BMW is a bit more effortless though.
Cabin, DS is noticeably quieter and feels bigger. Aesthetics wise, I love the fineline wood trim in the X3, but also like the leather contrast in the DS (almond/black). Honestly BMW interiors aren't the most amazing, so it's a toss up for me. I think both cars could use a splash of something on their center consoles though. Both vehicles have nice looking, firmish seats that are reasonably comfortable. The DS trumps the X3 with backseat leg room and cargo space, but I think we all knew that.
Tech, this is a toss up for me. The DS is my first car w/ touch screen, which I'm liking...although I do find the touch screen more distracting to manipulate while driving and get why MB/BMW stick to their guns with a control knob. The interface is well designed though and looks good compared to some other brand's touch screen systems. Everything works like it's supposed to, Bluetooth audio quality is great in both cars, which is a big deal for me since I stream everything from Google play. From what I've done with the Nav in the DS, it's nicely functiona and the voice control in the DS works better than my experience with BMW. But overall, both tech systems offer a ton of functionality. The X3 does have some nice tech advantages not possible with the DS - namely the HUD and surround camera system. As a side note, the audio upgrade with the DS is totally worth it, amazing sound and the subwoofer bumps.
MPG - My MPG after about 200 miles in is averaging around 24, which is about the same as the BMW. Only difference is that the BMW advertises better MPG than the DS. (I do a combo of city/highway/suburban driving, my wife drives the X3 mostly highway/suburban but in heavier traffic than me)
DS issues - Backseat started squeaking a couple days in, will bring in soon for the fix. The car vibrates a bit much when idling at a stoplight, not terrible, but it's more noticeable than my BMW.
Overall still very happy with the DS, the exterior looks soooo good. I love a lot of the little quirks it has (touch LED lights, sunglasses case, hidey hole etc) And has great interior space and functionality. However hopping in the X3 occasionally is not something I'll ever be disappointed doing