Landscape photographers are concerned primarily with low-ISO image quality—the ability to record fine details, wide dynamic range and accurate (or as-envisioned) colors, while shooting stationary subjects from a tripod. While wildlife photographers certainly appreciate good image quality, key criteria also include AF speed, high ISO performance and system ruggedness.
TOP: Samsung NX300, Fujifilm X-M1; FAR LEFT TO RIGHT: Panasonic Lumix DMC-GX7, Sony NEX-6, Olympus PEN E-P5. The original concept behind the mirrorless interchangeable-lens camera was to provide DSLR image quality without DSLR bulk. The image-quality part was easy: Just use a DSLR sensor—first, Four Thirds size, in the Micro Four Thirds cameras from Panasonic and Olympus, then, APS-C in cameras from Samsung and Sony, and later Fujifilm, Pentax, Canon and Leica.
Nature photography encompasses a wide range of subject matter, from landscape vistas to birds in flight. Naturally, some cameras are better for some types of photography than others. For example, most would prefer a pro DSLR over a "flat"-style mirrorless camera for birds in flight. But today's DSLRs and mirrorless cameras are quite good across the board, and you don't have to spend a fortune to get a highly capable nature photography camera.