I thought this was an interesting question. Let's take a look at Jeff Green today (year 8, middle of prime) and see what rank of player he would be on each of the last 10 championship teams. And I'm talking overall, not just in the finals, where a single player can have a hot or cold streak.
12-13/11-12, Miami Heat:
Definitely behind James, Wade, Bosh. Questionable Ray Allen in 12-13. Verdict: 4th/5th.
10-11, Dallas Mavs:
Definitely behind Nowitzki, Chandler. Probably behind Marion, Terry, Kidd. Close to Butler. Verdict: T-5th.
09-10, Lakers:
Definitely behind Pau, Kobe, Bynum, Odom. Possibly behind Meta World Peace. Verdict: T-5th.
08-09, Lakers:
Definitely behind Pau, Kobe, Bynum, Odom. Verdict: 5th.
07-08, Celtics:
Definitely behind KG, Pierce, Ray, Rondo. Close to Posey/House. Verdict: T-5th.
06-07, Spurs:
Definitely (far) behind Duncan, Parker, Ginobili. Ahead of Finley, Barry. Verdict: 4th.
05-06, Heat:
Definitely (far) behind Wade, Shaq. Likely behind Haslem, Mourning. About with Walker, Williams, Payton. Verdict: T-5th.
04-05, Spurs:
Definitely (far) behind Duncan, Parker, Ginobili. Behind Bowen. Verdict: 5th.
03-04, Pistons:
Definitely behind B Wallace, R Wallace, Billups. Likely behind Prince (same offense, Prince better D). About same as Hamilton, but really likely worse. Verdict: T-5th.
So really, he's probably the 4th-5th best player on a title team, unless either the team has a GREAT top 2 or a seriously good top 2 and then a bunch of Green-level guys tied for 3rd at spots 3-7 on the roster.