Usual Basics
Just as with dSLRs, you will want to consider the following "main" features of a camera system in addition to any gee-whiz features you find sexy:
- Sensor size and resolution (affects noise performance, and lens size/speed--the larger the sensor, the bigger/slower the lenses are liable to be to keep the system compact).
- Overall system breadth (lenses, flashes, etc.) filling your needs.
See also: How do lens lineups vary across Mirrorless camera systems?
No "Missing" Features
If you come from a dSLR system, particularly if you're a prosumer user, you will also want to make sure that features you're used to having and consider vital to your usage patterns, exist in the mirrorless platform you're looking at. A few possible gotchas, depending on the model/system, can include:
- Back-button autofocus
- Dual-wheel controls
- Viewfinder
- High-speed sync and wireless flash systems
- Tracking AF capability
Some of these features you may be willing to trade off for the smaller system or for a lower cost model. Some you may not. Make a list.
See also: Mirrorless camera vs. mid-range DSLR — how to decide?
Body Type
Another criteria that you don't have in the dSLR world is the body type of the camera. There are a few different types in the mirrorless world, that roughly boil down to:
- Compact-camera like (no viewfinder, but tilting or flip-out LED composition)
- SLR/bridge-camera like with a deep grip
- Rangefinder-like with a corner viewfinder, rather than a central viewfinder "hump"
The handling of each of these types of cameras is distinctly different from the others, and this is where your personal preferences are most likely to come into play. Do you prefer not smashing your nose into the back of your camera? Are you a left-eyed shooter? How much does a deep grip make a difference to you? Are you using long lenses? How small a camera system do you want? Did you want to pocket your camera?
Viewfinder
The viewfinder (if there is one) is another consideration. Does the eye relief work with glasses? Is it an electronic viewfinder or an optical/hybrid one? How accurate is the framing? How good is the refresh rate? How accurate the colors? Does it tilt?
TL;DR
My general overglib and oversimplified advice is go micro four-thirds, if your main concern is smaller gear and a larger array of glass. Go Fuji X if your main concerns are color and haptics, and you like the styling. Go Sony if your main concern is sensor performance or you have to have full frame.
Given the breadth of what's on offer, and how different these cameras can be, you may want to consider renting prior to buying to get a better idea of how these cameras handle for you.