Halgerda, I did a bit of both - tutoring my son directly and getting him some private lessons. I think the two are very different. Yes, I could help my son, and did go through old test papers with him, but with maths especially, my methods of doing things were at times very different to the methods he had been taught at school and half remembered.
He needed coaching from someone who knew what methods he had been taught at school so the tutor's work complimented the teacher's work, otherwise I'd have had one confused son.
Freckle - good luck and don't envy you going through it all again. I think you are right to get some coaching, as so many other children aer coached. FWIW, I also think that there's coaching and coaching - some children I knew had a private, professional tutor coming to their homes twice a week for one-to-one sessions and were given 11+ homework as well. And they had this this support for 2 years before the 11+.
My son went to a class onece a week for an hour. (Incidently I went with an organisation called The Extra Tuition Centre and it cost £50.00 a calendar month with free assessments, so a bit less expensive than a private tutor - there might be a ETC in your area) My son was taught by students (sixth formers and student teachers I'd imagine) - anyway, many looked under 20 years old. There were approx 10 children and 2 tutors, so no continuous individual attention and no homework was set. He spent the hour doing short practice tests which were marked by the tutors, who then went over any of the answers he got wrong. It was not particularly organised but it was something. He had this for six months before the 11+ so he had much less intensive tutoring than some of the others who sat the test.
He passed the 11+ with marks to spare, but didn't get super high flying results, so I was a bit apprehensive about how he'd cope at grammar school. So far, he says he feels he's at the level he should be - the standard of expectation is ok for him.