Baron said: "Clive is an outstanding individual and I worked very closely with Clive for six years. We had some fantastic times together but we have got to move on.
"We defined 25 separate parameters by which to measure all candidates. Clearly Clive has excellent credentials but Rob has strengths in other areas too.
"We had to take a balanced view across all parameters and determine who would be the best guy to take England forward. It is not about the 2007 World Cup, it is about 2011 and 2015. It is a long-term appointment."
Baron also insisted the RFU had not pre-judged Woodward's interest on the basis of some critical comments he made in the wake of his departure in September 2004.
Baron told BBC Radio Five Live's Sportsweek: "We decided right at the outset if Clive wanted to throw his hat into the ring he would be treated exactly the same as all the other candidates."