Garbz.
I am not sure what your original statement meant WRT to depth of field. An FX sensor camera produces pictures which have less depth of field than the same scene shot on a smaller format camera. To me, the biggest problem with the smaller-format cameras is that they *require* the photographer to use very shot focal length lenses in order to encompass something as mundane as a standing human being; the short focal length lenses used on DX sensor cameras lead to immense depth of field.
In-studio, with a DX format camera, one is often forced to use focal lengths in the 19mm to 35mm focal length range, which leads to backgrounds that are very much rendered in-focus--recognizable folds in muslins, dimples in seamless paper rolls, all sorts of annoying background depth of field goes with the small DX-format d-slr's images.
With a full-frame camera, one will use longer focal lengths for identical image sizes and angular views, and the depth of field will be shallower; less will be in-focus behind the subject, even with the subject rendered the same,exact height. The ability to throw the background decidedly out of focus, the ability to easily achieve foreground/background isolation, are the two main reasons professional wedding, editorial,and sports photographers often prefer full frame cameras to those with smaller sensors.
The smaller the sensor, the deeper the depth of field, per angular view; creating THE SMALLEST EVER film format, the Kodak Disc format, was done by Kodak as a deliberate engineering solution to solve the problem of finding a way to create a camera that would never,ever need to be focused. By making the capture area incredibly tiny, Kodak created a camera that could us a very short focal length lens that would have almost infinite depth of field when focused at about 3.5 feet; the same thing exists with todays Point & SHoot digicams--by using a small capture area, they use short lenses for every angular view they capture, and they have HUGE depth of field. APS-C cameras render images with greater depth of field than 24x36mm sensor cameras do, per angular field of view, in real-world conditions.
What I find ironic is that the 4/3 sensor format is almost the same size as the now-defunct 110 cartridge film format, which was the smallest format in common use before the Disc format was invented in the early 1980's.