I'll share my rule of thumb for deciding between these two reasons for a close vote. I don't urge it on anyone but it gives me some cognitive harmony.
If the Question lacks essential setup or clarity to be reliably answered, then I use the "Needs details or clarity" close reason. This for me means a more severe deficiency in the Question's present form, making it something of a guessing game as to what the actual problem is.
If the Question is coherent but lacks sufficient context to show that the poster digested the problem and is prepared to learn from a correct Answer, then I navigate to the submenu for a community-specific reason, "provide additional context".
Admittedly this is inconvenient, but it results from the StackExchange architecture that creates mostly uniform close reasons (and boilerplate explantions) for all communities to share. So the innovation of community-specific reasons (in this case requiring the asker to have thought through and researched the problem before posting) was done by adding the submenu.
Of course this still leaves some gray areas. A Question posted from a book or classroom assignment may often lack key indicators that the poster made an effort to research it, e.g. not showing how a key notation or concept is defined, and may also be deficient (IMHO) because it gives no clue as to what level of material is being covered and what the problem might be intended to reinforce.
Largely the rule helps my level of comfort in choosing between the alternatives. Where both reasons seem applicable I tend to choose the "Needs details or clarity" not because the menu option is easier but because it indicates the more severe problem. I suspect in many cases users fail to give context because they worry it will betray their lack of understanding. But really we want to address their level of understanding with skillful explanations, and often I leave a comment to that effect.
