Jerome,
Would you care to mention them?
In a nutshell:
-higher resolution. Many "reviews" try to have us forget that difference by publishing pictures reduced to the smaller resolution of 24x36 cameras, but one should not forget that digital MF resolution starts where 24x36 stops. MF is 40-80 mpix. If one needs that resolution for huge enlargements (and some people do), it is either MF or stitch.
-better lenses at medium apertures. MF lenses are bigger (even considering the bigger image circles) and routinely use more elements. The reasons are mainly commercial: the manufacturer can charge more money and customers do not insist on very fast apertures on expensive lenses. The optical engineers can therefore optimize for better correction of aberrations at medium apertures and better corner sharpness.
-different photographic practices: MF users often shoot in studio and control light better. Higher average production values translate to higher average quality in the public's mind (this is not inherently due to the cameras, but contributes to the idea that "MF is better" nevertheless).
-better bokeh: that one is counter-intuitive. MF needs smaller apertures for the same depth of field. Moreover, MF users tend to use larger depth of field than 24x36 users for portraits. In the end, MF portraits may be shot at f/5.6-f/8 when 24x36 portraits may use f/1.4-f/2.0. Secondary optical aberrations are insignificant at the apertures used in MF practice, while they change the out-of-focus highlights shapes and color in 24x36 practice. Bokeh is very dependent on aperture.
-slightly better color separation: 24x36 cameras are a different compromise which includes optimization for less noise at high iso, leading to less selective primary filters, a hotter adjustment of their meter and different choices in the internal treatment. MF manufacturers optimize for studio practice where there is plenty of light. The post processing chain is calibrated for more flattering skin tones, since this is part of their core market. The A-D converters and meter are set up to keep more of the information in the highlights (at the expense of worse shadow noise).
There is nothing inherently different in a bigger sensor (except, usually, higher full well values for bigger pixels but MF does not always have bigger pixels, just more of them), but there are practical consequences in choosing a bigger sensor that leads to different choices as to lens, used aperture and calibration. These are, in turn, responsible for a slightly different rendering of MF.