As I understand it in the normal 4x4, the 4x4 system does not engage until the front wheels lose traction and so the power is then distributed to the rear too.
In the Cross, there is the dial near the handbrake that allows you to put it straight into 4x4, negating the need for the fronts to lose traction first as mentioned above. Useful if you have a muddy bank ahead that you need to go up, but otherwise I can't see any other use for it.(
Not quite...
The Cross has a dial, which has three settings. The first - 'auto' - does 'nothing', and is the same as the 4x4 model with no buttons pressed. As you say, in this mode, traction has to be lost (only for split second) to engage 4 wheel drive, and it will revert to 2WD as soon as it can.
The second setting, marked 'off road', has the same effect as pressing the 'ELD' button on the 4x4 (this forces 4x4 engagement and allows the ELD to operate if needed, but only up to 30mph. It also disables the ASR - part of the traction control system)
The third setting is unique to the Cross, which is the Hill Descent Control. However, the 4x4, especially with the diesel engine, has great hill-slowing potential when used in bottom gear with feet off all the pedals.
Ride height: the Cross sits 6mm higher, which is (as others have said) all because of the slightly taller tyres
Approach angles: the Cross's cut-away front bumper allows a (slightly) better approach angle, but I've never yet had an issue with my 'regular' 4x4 along Hertfordshire's green lane public byways.
The most expensive difference (which I don;t think others have mentioned yet) is the Cross has the full automatic climate control, as opposed to the 4x4's manual air con.
There is one more difference, this time in favour of the 4x4. The Cross has 'all season' but road-biased tyres (Goodyear Vector 4). The 4x4 has 'true' winter and off-road-rated tyres (better mud grip and - I believe - intended to be more durable off the tarmac: Continental CrossContact Winter). I have been surprised at how good these are all year round, and they last me 30,000 miles (replaced at 3mm to retain snow grip - which the past couple of weeks have shown to be phenomenal!)
Here was Fiat's own press release from the launch of the Cross:
http://www.fiatpress.co.uk/press/article/the-new-fiat-panda-cross-a-car-like-no-other