Even pricing between the two is similar as tested in this comparison with the BMW M6 coming in at 123,600 Euros and the Jaguar at 129,900 Euros. Keep in mind this is European pricing which differs quite a bit from that in the United States.
So what about the performance? Well, the M6 has the edge acceleration wise. 0-160 km/h (or 0-100 mph) is recorded in 8.2 seconds. This same takes 8.8 seconds in the Jaguar, still very fast but slower than the M6. 0-200 km/h (124 mph) takes 11.9 seconds in the M6 and 13.5 seconds in the Jaguar. Edge, M6.
What about handling? Well the weights of the cars are actually pretty close to one another. The M6 tested at 4184 pounds and the Jaguar XKR-S at 4032 pounds. The Jaguar is lighter by just over 100 pounds but neither is a lightweight, both over 4000 pounds. Even with the increased weight the M6 manages a higher slalom speed at 69.3 km/h versus 68.0 km/h for the XKR-S. The roadcourse also goes to the M6 with a laptime of 1:38.4 versus 1:40.9 for the XKR-S which is a pretty significant difference of two and a half seconds.
The BMW takes the comparison fairly easily and outperforms the XKR-S everywhere even including emissions and fuel economy. The new M cars may not feel the same but they still perform at a high level.