I’ll be expanding on this topic as time goes on.

In my view, these are the key points (for me .. and in no particular order) :

• Is a housing available ? (stating the obvious)
• Does it have Aperture / Shutter / Manual priority modes ?
• Megapixels / resolution ?
• “Shutter lag”
• Shot-to-Shot time
• Batteries ?
• Shot capacity
• White balancing options
• RAW format ?
• Zoom range
• Lens
• Macro mode
• Strobe (flashgun) availability
• Options – add-on lenses, filters etc.
• (recent feature) image stabilisation
• “My mode” / user presets

Of course, some of these “trade off” against others.
For example, shooting in RAW mode will slow down shot-to-shot, and will also reduce the number of images you can fit on a memory card.