From my personal experience, this is what I can tell:
Using a flat/softer material lace is better. This allows for the lace to hold on the knots.
I have laces made of harder material (Nylon types). The knots on these tend to come off when they get wet. Mostly because they don't grip each other.
Avoid laces which are cylindrical, they do not hold knots well.
When they are tight enough to prevent movement within the shoe/boot but not so tight that it causes discomfort.
A little too loose is actually worse than a lot too loose. A little too loose will guarantee a blister, while a lot too loose will reduce your ankle support.
how tight is too tight?
Probably something that doesn't come off while walking in tall grass, but does come off quick when you want it to, also fast to tie up again is the knot you are looking for.
I usually prefer Ian's Secure knot. Such a brilliant link!
There is a pair of shoes which have a slightly longer laces which I deliberately didnt ...
I find that the best shoelaces are the wide, flat and fairly soft ones - no special plastic coating, just canvas. They stay together the best and can take a lot of punishment. Accidental strong knots are also easier to undo, since it is easier to get a finger behind an edge due to its flatness.
The ones on the picture here seem a bit too shiny, so perhaps ...