Perhaps the main advantage of mirrorless systems is that they can be designed to be much smaller than DSLRs. While image processing and sensor technologies vary across DSLRs and mirrorless cameras, the fact that many mirrorless models use the same APS-C and full-frame sensors that you'll find in DSLRs means that neither system has any inherent advantage when it comes to image quality. Indeed, this is the main sell of the system: the same size of sensor and image quality as offered by a DSLR without the bulk.
The main reason for this is that DSLRs have a mirror just behind the lens mount and an optical viewfinder above this, one that receives the light reflected off this mirror, whereas mirrorless cameras do not. On entry-level DSLRs this doesn’t have any significant effect on weight, but more advanced DSLRs are typically designed with a glass prism in their viewfinder chamber, which makes them heavier.
Designs in both mirrorless and DSLR systems vary considerably, particularly in mirrorless cameras where there has been a greater number of manufacturers pitching in with their contributions, but DSLRs are constrained by the need to have these two components. As mirrorless cameras do not, manufacturers have been able to make certain models and their accompanying lenses small enough to be pocketable, something that can’t really be said of any current DSLR.
Of course, there are often trade-offs in making a mirrorless camera so compact, such as the size of the sensor and battery life, together with the way a camera handles. Nevertheless, there is far more freedom in designing these mirrorless systems to make better use of space than there is with DSLRs.
Although it’s possible to buy mirrorless cameras fashioned like DSLRs, the vast majority are not. For a mirrorless camera to present a size advantage over a DSLR, the easiest design decision is to drop the grip, or at the very least to replace it with something that doesn’t protrude from the body to the same extent.
Whether this design suits you or not depends on largely what you plan on shooting and what lenses you plan on using. Longer, heavier, wide-aperture lenses can look comical on smaller, grip-less bodies, and will also be unbalanced in the hand. Some mirrorless brands don’t even offer cameras with grips that are defined enough for weightier lenses, although it's often possible to buy these as an additional accessory.
Another thing to consider is how you are likely to operate your camera. Junior-level mirrorless cameras are designed to appeal to an audience that’s more used to smartphones and tablets than traditional DSLRs, and so you’ll find fewer physical controls around the body and a greater reliance on the touchscreen to perform many functions.
Touchscreens are now, of course, widely found on DSLRs, but they are arguably less important here as they are not active when you have the camera up to your eye – ie when capturing images conventionally. Instead, they are used for setting focus and certain shooting options when using live view, as well as for video and when reviewing images.
Small bodies also means small controls, and users with larger hands may not find those on some mirrorless bodies to be comfortable. This extends to touchscreens too, with virtual buttons and controls often too small for then to be keyed comfortably.