Unfortunately Canon has nothing even remotely comparable to the Sony RX100 II at the moment.
By all reports the RX100 II is a great compact camera. However, there are some significant drawbacks when compared with Canon Rebels and other current APS-C cameras:
1) Sensor size: The APS-C sensor in the Canon Rebels and 60/70D is roughly 3 times larger than the Sony sensor (APS-C 22.2x14.8mm = 328 square mm vs. Sony RX100 II 13.2x8.8 = 116 square mm). Larger sensors allow for better depth of field control, reduced noise and generally better image quality.
2) Fixed lens vs interchangeable lens: The Sony has a fixed (non-interchangeable) 28-100mm FF equivalent lens. The variable aperture goes from f/1.8-4.9 which equates to f/4.9 to f/13.2 on a full format camera. Not only is the focal length very limiting (28mm isn't that wide and 100mm isn't much zoom), but the maximum aperture is limiting like a typical P&S camera. There will be almost no ability to isolate a subject with a shallow depth of field.
3) The Sony also as an electronic viewfinder vs. the optical viewfinder on the Canon's. With an OVF you are using your eyes to evaluate the scene in front of you, EVF's see a very limited range of exposures compared with the human eye and are not as good in bright light.
Those disadvantages are significant enough for me not to be interested in these small sensor cameras, but I'm sure they appeal to many others who are OK with those limitations.
Personally, I like to have the ability to change lenses and have focal length and maximum aperture flexibility.