Lame answer, but I think it depends on a LOT of things.
1. Can your team get hot in the playoffs and win it all as currently constituted? Generally, if you can make the playoffs, anything can happen.
2. Can your team get hot in the playoffs and win without <Player A>? <Player A> being a veteran player that you're considering moving for some kind of future equity. It's a bonus to get some future equity but still have a chance to compete this year if you just get hot at the right time.
3. How desperate are the other managers in your league to a player such as <Player A>? Like if I have an older player, let's say Harrison or T.O. or something, I'm not going to trade them just because they're old and my team may suck - if you can get offers that represent value, then do it. But don't lowball because you want to "get young" - TO/Harrison is worth more on your team next season than a crappy rookie pick or something will be in the next 3 seasons (most likely).
And to a lesser extent...
4. Project what kind of player you can expect to add in the rookie draft next season with your current pick, and with whatever pick you're considering moving too. For example, I'm in a couple 16 team leagues - if I think my pick will be around 11th or 12th, which might be the 5th or 6th RB, 2nd or 3rd QB, or a top IDP, then I can let that pick go earlier if another team "blowing it up" ignores # 3 and is willing to sell an impact player rather cheaply.