DSLR vs. Mirrorless Cameras
Mirrorless cameras have until recently lagged behind the DSLR cameras in performance including and in particular the ability perform fast focusing. This has change beginning with the new Sony A-series cameras.
The first obvious benefit of the mirrorless camera is its small size. With modern electronic viewfinder framing the image is almost as good as with a DSLR camera. The additional benefit of the electronic viewfinder is that it can also be used in video-mode, which is a huge benefit over using the LCD-screen. Having to rely on the LCD-screen in outdoors conditions can be very difficult, and therefore the electronic viewfinder can be a deal breaker in selecting a mirrorless camera over a DSLR.
Full Frame vs. Cropped Sensor
The full frame lens on a cropped sensor camera will act as if a digital zoom was applied to the image, because only part of the image circle will be used by the sensor. A 50mm lens for example will create images similar to a 75mm lens on a full frame camera. However, the actual 75mm telelens on the full frame camera will be somewhat sharper, but have a shallower debth of field. Lenses designed for full frame cameras can be used on cameras with a smaller sensor. The revers is typically not possible unless the camera has special provisions to accommodate a lens design for a smaller sensor. If you plan to upgrade to a full frame camera in the future then only buy lenses designed for full frame cameras.
Image stabilization in the lens or image sensor is always good when slow shutter speeds are used. If you produce hand-held videos image stabilization is critically important. Most DSLR cameras rely on image stabilized lenses for good results. Pentax DSLRs applies stabilization in the image sensor, but in newer models only for still photogtaphy. Videos use digital image stabilization, which tends to be inferior. Internal camera stabilization is good when using older non-stabilized legacy lenses or newer third party manual lenses. The new Sony Alpha cameras have all inage sensor stabilization, which works well also in the video mode. Best stabilization can be achieved with a steadicam or battery operated gimbal, but these are not always convenient to use.