There are lots of challenges for the Sims 2, Sims 3, and Sims 4, but today I would like to talk about fitting challenges for each game that would be difficult to transfer over to other games because of the way the game is constructed.
In The Sims 2, time and aging both pass on residential lots. If a Sim goes to a community lot and returns home, the Sim will return at exactly the same time. This is actually very similar to traveling to a sub-world in the Sims 3 in which time and aging will be frozen in the main world as the Sim visits the sub-world. For this reason, the Sims 2 would be ideal for doing rotations, and the family albums and neighborhood albums create a more cohesive story of what happens in the game. With that said, a fitting challenge for the Sims 2 would be the Build-A-City-Challenge. The BACC involves a lot of detail and micro-managing and rotational gameplay.
In The Sims 3, there is an open world, and one challenge that really takes advantage of the open world would be the Runaway Teen challenge, or if you choose to start with a Young Adult, the Homeless challenge or Rags-To-Riches challenge. You can also avoid adults and elders in the Sims 3, because they actually look different from teens. You can technically do this in the Sims 4 and the Sims 2, but without an open world, what's the point with foot-travel?
In The Sims 4, weight loss/gain works completely differently from what it was in the Sims 3/2, so if anything, you can do a weight loss challenge and get a super-fat Sim lose weight or get a super-thin Sim to build up on muscle and fat. In The Sims 4, you are most likely controlling one Sim at a time, but then the uncontrolled Sims seem to have the autonomy to do stuff and not kill themselves; so for that, I think another fitting challenge would be the Three Little Sims challenge in which you have to control just one Sim at a time and let other Sims run on free will. The Three Little Sims challenge would be difficult to transfer over to the Sims 2, because Sims 2 Sims are dumb and will kill themselves by fire or hunger; and in the Sims 3, you would just miss out on a lot of wishes and opportunities for the uncontrolled Sims so the Sims' LTWs are harder to fulfill. In The Sims 4, how you live your life doesn't really matter, and all Sims will die the same way (unlike the Sims 2 and the Sims 3), so even if you mess up the lives of those Three Little Sims, there are no bad consequences.