I can't say anything about the other person, but Ms. Warrior would be a disastrous pick, IMHO. I had some contact with her when she was CTO at Motorola and I came away from that experience thinking she was:
1. Was a poor leader
2. Did not consider opinions other than her own on making decisions.
3. Was really not very knowledgeable
4. Was only out for her own advancement
Perhaps these are the attributes of many successful executives, but don't strike me as qualities you want in a civil servant.
Did you ever have contact with a person of real power/wealth/influence and come away thinking "How did they EVER get to where they are?" The older I get, the more I think success requires some work + many connections + a lot of luck.
It looks like the last might strike Ms. Warrior here again pretty soon.