What sort of help one can expect from a public school’s busy guidance counselor?
That they write a recommendation for your child and upload it to the common application. (Assuming you’re talking about help with college issues.)
Do they care more for top students or its all the same wether it’s a simple state university auto admit vs complex game of getting into an Ivy?
The answer to your question will vary from school to school and from guidance counselor to guidance counselor. There is no one hard and fast rule. I would suggest that if you want help from the guidance counselor that you ask to set up a a meeting about college planning and solicit his/her advice.
Some schools have big group help - usually how to apply to state schools, deadlines, financial aid. They will probably go over the rules about recommendations (how many, lead time needed), transcripts. Go to these meetings if they have them.
Some counselors are terrific and can meet with each college bound student to pick out some schools, but most really don’t have the time to do one-on-one meetings and build a list of schools, double check testing schedules. You really do better if you have done all the research and just ask the GC for opinions or to check facts.
It really does depend on the school and likely on the kid applying. At our HS each junior and family have a meeting with the GC to pick out schools and go through the process of applying. The GC gave some guidance on match, safety and reach schools (although for oldest was more pessimistic than was warranted; my guess is a student did poorly in admissions the year before). The GC for my youngest wanted the student info sheet and parent brag sheet before school ended in June so she could work on the counselor letter over the summer. In our HS, the GCs do not allow parents to see teacher recommendations and as far as I know, will not tell the family if a recommendation is not super positive. I know from a relative, however, that the GC did provide info about the different teacher recommendation letters (although his kid did not get into any reach schools). With three kids and more than one GC each for two of them, I have been generally pleased with the GCs. However, most of the effort on coming up with a list came from us not the GC.
I would think there is more work involved by the GC in an application for a private college than an auto-admit state school. But I also think the GC only writes one letter of recommendation that is sent to all of the schools. I can’t imagine the GC writing a separate letter for each college. For a student that has the stats for a super elite college, the GC would hopefully know the kid and be able to highlight his or her achievements in light of what others have done and how the student stands out. The student and parent brag sheets are also important in that regard.