Mavs: They have two legitimate options: go full tank, or make one last run with Dirk. Neither option is particularly bad for their future. Either they give it their all and cede a pick in the 11-18 range, or they accept the end of the Dirk era and rebuild using a top 7 pick. Given the moves they've made, it would be pretty hard for them to bottom out IMO, so I see them going for the playoffs.
Nets: The Nets options are slightly less favorable for them: attempt to win as many games as possible just to spite the Celtics, or bottom out and focus on developing young players and finding ways to acquire draft currency from other teams. If they try to make the playoffs, it's very possible that they're still terrible and gift us a good pick, causing the season to be completely lost. At least bottoming out would give them something to build with in the future. Ultimately, I think the Nets should trade Lopez and Young once their contracts allow for it; they both have some value and would be able to bring in some nice future picks IMO. The picks which we have are a sunk cost; it just doesn't make sense for the future of the Nets franchise to try and spite us. However, I think the Nets will not take the prudent course of action, and will choose to push for the playoffs, ultimately falling short; trying to win games can prevent you from being a bottom 3 team in the league, but beyond that, inferior talent and depth won't win games.