I get this question often by people who are looking to get started with photography or when they are travelling and want something better than a smartphone for recording their journey. This choice is always influenced by the image quality. This is only logical, why would you want the inconvenience of having to lug something extra if your smartphone can already take pictures?
People have to be aware of the fact that better cameras don’t necessarily give better photos. A high resolution, clean image of some random person who happened to be in your shot isn’t going to excite anybody. Nevertheless, if you fancy yourself a budding photographer who needs a tool to flex your creativity, here are some considerations.
What class of cameras are you going for exactly?
1. Your ubiquitous point and shoot
2. Large sensor compact camera
3. Compact system camera, mirrorless camera.
4. Digital single reflex camera (DSLR)
5. Rangefinder
All the choices above assume that you are shooting in digital, not film, which would be another topic altogether. Let’s discuss the pros and cons of each category.
1. Point and shoot sales are dwindling faster than food in front of a ravenous boar. Why? The rise of smartphonography has been identified as the main reason behind this. Smartphone cameras triumph in that they offer the ultimate convenience. As Chase Jarvis states, the best camera is the one you have with you. The camera most people are likely to have will be their smartphones, thus negating the need for a dedicated point and shoot. Image quality also isn’t too far off with the advancement of smartphone camera tech. The main benefit for compacts is the optical zoom rather than the digital zoom found in phones, but again, with phones boasting increasing MP counts, this advantage could be wittled down soon.
2. Large sensored compact (Sony RX1, Fujifilm X20, Canon G1X mark II, Nikon Coolpix A, Pentax GRD)
This is where things are currently heating up in the camera market. Many manufacturers have reoriented their product strategy to focus on high impact products in this market segment.
The large sensors found in these cameras give users cleaner images at high ISO, not to mention better dynamic range. Oftentimes, extensive manual control and the ability to show in raw also distinguish this class of cameras from smartphones. These cameras are often the choice for users of DSLRS who need a reliable backup for travelling light.
3. Mirrorless (Sony A7, Olympus OMD and Pen cameras, Panasonic GH, GX, GF series. Nikon 1, Canon M)
The current revolutionaries in the camera world. Advances in this field can get people more excited than free flow beer at Zouk. Mirrorless cameras boast large sensors, manual controls, excellent ergonomics, performance and interchangeable optics, all in a small body to boot (generally, though I know I’m pushing it with the GH cameras). The moniker is due to the lack of a mirror box found in DSLRS that allows for through the lens viewing (ie, what you see is what you get) .
The size advantage and comparable performance gives this class an edge over DSLRs, with sports and high speed reportage being the only weakness of this camera class.

4. DSLR
The venerable Digital Single Lens reflex, so named due to the mirror that flips up during image capture. For so long this has been the go to camera of choice for working professionals and enthusiasts. Many of the qualities of mirrorless cameras also apply here. The main issue, of course, is the sizd factor. Nobody can say any DSLR with a mounted lens is pocketable (except maybe doraemon)
To me, DSLRs still have an edge in ergonomics and field usage, especially for people with large hands and for those working in harsh conditions. The flagship products and or enthusiast oriented models offer weather sealing and can take quite a beating. My Nikon D3 has been dropped, used in heavy rain, took a mild dunk in water, and yet still churns out high quality images time after time.

5. Rangefinder (Leica M9, M240. Fujifilm X series cameras like X-Pro and XE)
These offer a different experience altogether. They are usually not speed demons, as compared to the flagship DSLRs and Mirrorless Cameras. What they offer is stealth and well appreciated ergonomics. I have yet to enjoy a Leica, hence am unable to comment on them. Friends who do own one, however, rave about them enough that my interest is piqued. I have, however, used Fujifilm Rangefinder cameras and have found the experience very enjoyable.