Hiring managers, generally speaking (for any level, department, etc.), do you give preference to candidates who send a follow-up/thank you note after their interview?

It's not the fact that they sent a note (or didn't) but whether the content is compelling  - for instance, they include further details adding to a previous discussion or they ask an intriguing question.  In that case, my interest would be piqued.  Engagement and curiosity (not so much etiquette) wins the day!