Here are three factors that are clearly important for me:
First, Reliability and Robustness. This is the one that is most obvious, and is probably over-played, particularly by manufacturers justifying inflated prices becuase their device can withstand a forty-foot drop or submersion in water. But, in an emergency situation, you do want the best chance possible that your tool will work just as it always has, and will not flake out on you. It is interesting to note that reliability and robustness tend to be at odds with flexibility. A good example is my hiking GPS - a Garmin Rino 650. It only does one thing - show and track my location on a map - but it does that very well, and it always works. It always operates the same way when I turn it on, it always finds the satellites quickly, and it always shows the information in the same, simple way. Plus it's built like a rubber brick. In contrast, the navigation app on my smartphone is much more flexible - I can do all kinds of cool downloads of different kinds of maps, overlay traffic updates, find the nearest pizza store and so on - but it is not reliable or robust: sometimes the app requires updates before I can get it to run; sometimes the internet connection doesn't work; sometimes the app freezes or crashes. And if my phone gets wet, it's toast.
Second, Intuitiveness. Intuitive means that it works exactly as you’d expect, that working with it is straightforward even in a high stress situation. It means you spend your time thinking about what you are doing with the tool, rather than the tool itself. For electronic devices, that is sadly a rather rare property. A stark example here is given by two two-way radios I own: a Baofeng UV-5R (a super cheap, but surprisingly good chinese VHF and UHF radio), and a Racal 25 (a once expensive VHF radio used for military and wildland fire operations). Both radios are field programmable, meaning you can enter in the frequencies from the radio instead of with a computer. The Baofeng is super radio in some ways, but how to program it is almost impossible to remember, even in a low-stress environment. Conversely, the Racal just seems simply and cleanly designed to solve the problem, and frequencies can be entered and changed without even a glance at an instruction manual.
Third, disposability. This means I don't care too much if it gets scratched, or even ultimately broken, in the line of duty. This is why some of the "highest end" stuff simply doesn't make the cut even if it has the best specs - I'm never really going to want to take a $2,000 radio (that I paid for with my own money, at least!) into a rough situation.
So what other factors are there? Please leave any suggestions in the comments!