There is a disadvantage due to the sensor size, everyone will say that. While true, it is actually quite minimal. Obviously, it varies between models but a recent m4/3 camera compares to a recent one with an APS-C within one stop in terms of noise, and it is rarely visible until ISO 800+. Here is how the differences looked last year. All these models had one successor since.
The only serious difference is actually speed. All the current m4/3 cameras use contrast-detect AF which is slower by a noticeable margin to phase-detect, which is used by DSLRs. There is a small but noticeable display lag as well because the LCD or EVF works electronically (not a the speed of light as with OVFs). With subjects that move slowly this is not a problem at all, but for action it can be.
There are obviously more differences but the remaining ones tend to be more specific to certain types of photography. Certain features are not available yet in m43 too, such as weather-sealing, sync-port, GPS, support for AAs, etc. You'll have to investigate which ones impact you depending on your photography style.
The number one advantage is reduced bulk, so a smaller and lighter total system. Micro Four-Thirds camera are smaller than DSLRs but the savings also translate to lenses. Each lens is smaller, so the size and weight you need to get a comparable feature set.
The fact that the lenses are smaller also lets them design lenses with a bigger maximum apertures. This applies to full-size Four-Thirds and Micro Four-Thirds. The best example if the two Olympus F/2 zooms, the 14-35 F/2 and 35-100 F/2. To use these on a Micro 4/3 camera you do need a small adapter.
Going back to Micro 4/3 specifically, the shorter distance of the mount to the sensor means that you can adapt much more lenses from other mounts to Micro 4/3 without losing focus at infinity. A particularly interesting adapter exists that also adds a shift or tilt mechanism between the mount and the lens (sorry, do not remember who does this).
The fact that those cameras were designed to show a live-image means that there is no cost to see a live-view compared to current DSLRs. As of today, no DSLR has a live-view that does not reduce its performance somehow (usually AF speed but Sony DSLRs compromise VF coverage instead). This is likely to disappear over time, but for now you can count on it.
Eye-level shooting of video is not possible with a DSLR since video requires a live-view feed. Several Micro 4/3 camera will provide this using an optional EVF.