We did St Petersburg with Red october and they were SUPERB.We saw far more than the official ship's tours and the trip was tailored to our needs (we had kids with us and they helped us keep it interesting for them). We were a party of six and therfore had our own minibus bur smaller parties can be "matched up" to fill the car or bu.
Have visited St Petersburg many times and would strongly advise not to do an independent tour. The cost of visas, the unhelpfullness of Russian officials and the distance from the berth to the city. If you can read and speak a liitle Russian that might change things - but only a little IMHO.
This question has been raised a number of times recently so I suggest you scroll to the top of this screen and type the word 'petersburg' into the keywords box within 'Find a Question' and press search. Your main concern should be to ensure you don't have to apply for personal visas for entry into Russia (unless you really want to!). P&O will cover you with a block visa for going ashore on their own tours and certain local companies do similar. The postings on this site should explain this in more detail.
If you want to be independent from the hoards from the cruise ship suggest you sign up for a private tour operator like Alla or Red October or Denrus. Parties limited to 20 or 30 pax, you see a lot more, and it works out cheaper than the cruise tour prices. I am booked with Alla and it is $300pp for a full 2-day tour limited to 20 pax only.