It is more of what kind of h.s. experience you are looking for then who is going to review you.
If you want to be entirely independent in what you do then board review is best as youc an truly do what you want and just go for the review that is friendly and simply is veryfying if you did provide
"regular instructions in the required areas of studies"...
Board of Education review is not complicated process, it is more imporant what you teach your child and to make sure he or she is not going to have any problems when / if eventually re-entering PS system. It is fairly easy to satissfy the needs of the interview if you indeed provide regular instructions for your child.
Umbrella system might have some benefits in certain regards but this is should not be your influence on how you school your child. If you are more of independent mind and wants to maintain it then board review is best, if you like to be part of a group and still having to send your reports to the system as reqired then the choice is yours.
I personally would still go with board review even if I was using an umbrella group as I would like to have sure feedback as and if I am complying with the requirements but this is only because I plan to send my children back to system in five years so I feel more confident that I have regular approval of the public system to what I am doing is on the same page. If I did not plan to send kids to p.s. then things might have been different.