I am coming to the end of 10 years experience of two of the prep schools -won't name names - and I would say it depends on a few things.
If you are happy to pay the fees I would look at all the schools and see how you feel about them. No matter what opinions other people have you have to be happy with your choice and only you know if your son could be happy there. All the schools should let your son spend a day / half day with them with no obligation on your part - you shouldn't get any "hard sell".
Birkenhead Prep doesn't prepare for 11+ as they want you to continue on to the Senior School.
Consider travelling distance if one is closer to home that would make life a lot easier believe me.
Another option you have is if you are near to a good state school then send your son there and tutor for the 11+.
I could go on (an on) but don't want to bore you.
Hope this has helped a little, I remember well the pressure of wanting to do make the right decision.