OK, I've attempted to compare apples to apples (using MotorTrend data), but there seems to be no publication that has published much about the relative performance of the M340i xDrive to the M440i xDrive, other than 0 to 60, braking, etc. Personally, I think MotorTrend's figure eight test helps, but they tested an M340i RWD, not xDrive. Still, here's a snapshot look at these:
I would love to see the M340i xDrive's figure eight time and grip. Of course, tire selection makes a big difference here, and I'm not sure what tires were on each car.
Subjectively, what I can say is that, the M340i xDrive, like most cars (even RWD cars), show some understeer on initial turn in, especially with early throttle. As most of you know, the car does rotate, and more so that other AWD cars I've driven. I suspect the M340i xDrive is at least 53/47 (and perhaps 54/46) in its weight distribution, since the RWD, as tested by MT, is 52/48 and the M440i xDrive is 54/46. You'd expect this would make a difference in its handling, and it probably does, but most of us mortals won't find a noticeable difference in 1 or 2 percent in either direction. That's even truer when considering the torque vectoring of xDrive.
I'd be shocked if the M340i and M440i, both in xDrive configuration, handled substantially differently. I'm guessing that there's simply a different expectation of a 2 door coupe, especially now that it's been given its own model designation (4 series instead of 3 series). But remember where the 4 series came from. It was a 2-door 3 series. In most ways, it still is. [Insert grille comment here.]