Who actually writes a strong one

The instinct is to ask the most senior person who knows your name. That is usually the wrong choice. A letter's strength comes from specific evidence — an anecdote, a piece of work the writer read closely, a judgement they can defend if asked. A head of department who taught you in a hall of two hundred can confirm that you existed and did well, and little else.

So rank the people you could ask by how much they have actually watched you do something. A tutor who marked four of your essays. A supervisor who saw you handle something going wrong. A manager from a summer job. Any of them can write something a committee has not already read a hundred times. Seniority is a tiebreaker between two people who both have something to say — not a reason on its own.