A couple of things:
First, I think the team would give him 4 years, $20 million. Rumor has it that we're willing to go 3 years, $18.1 million, while Posey is asking for 4 years, $25 million (or even a five year deal).
Second, there is a major difference in the revenue of the Celtics versus the Knicks. The Knicks brought in $196 million in revenue in 2007. Their ownership (Cablevision) owns Madison Square Garden, where they make a killing on gate receipts and concessions. Despite their poor record, the Knicks are considered the most valuable franchise in the NBA.
The Celtics are much farther behind. Their revenue for 2007 was $117 million, nearly $80 million less than the Knicks. The Celtics don't own their own arena, and have a lease that doesn't allow them concessions money. As of last year's Forbes list, they were the 11th ranked franchise in the NBA in terms of valuation.
Link.