I understand this is a subjective question, so I apologize if it needs to be closed, but I feel like it comes up often enough for me to wonder if there is a general preference for one form over the other.

Obviously, the best answer is "refactor the code so you don't need to test for falsehood" but sometimes there's no easy way to do so and the "else" branch is simply to continue processing. So when you must have an "if not false" construct, which is the preferred standard:

The not operator

if(!value)

Or the test for false

if(value == false)