I sincerely think each world is different. As I am evaluating whether or not I am going to re-sign a player, I look at my farm, the trade block, and current year free agency to see how replacable he is. If the player has something unique that I look for, I may go to free agency and query four years out to see how rare my guy actually is. If the guy I have is average, but he has ratings that I prefer (ie Maybe I like guys with contact, speed, and right split) - are there guys out there that play the same position? If so, what will it take to get that guy on my team to replace my current guy? If it is more than what I'm willing to give up, I re-sign my current player.
Also need to consider his position. Typically, premium defensive positions (SS,2b, CF, 3b) lose their value more quickly than 1b or corner outfielders unless they are excellent hitters. But, if they were excellent fielders and also excellent hitters, it should be a no brainier to keep him and just switch his defensive position where needed. Those 1b/corner outfielders start to slowly lose power in their late twenties. Then around the age of 33-35 they get huge power decreases each year. If the players value is mainly power, you'll need to evaluate that as well.