Lazy/ActiveThe primary differences between Lazy and Active Sims come in the form of quicker need decay. Active Sims will require more carbs to keep up their high-impact lifestyle, meaning that they'll need to fulfill the already-tricky Hunger need more often than other Sims. Lazy Sims, on the other hand, dissipate their Energy and Comfort needs rapidly, which can lead them to automatically nap when they feel run-down.
Beyond those basic differences, though, it's generally better to have an Active Sim than a Lazy one. There aren't any social consequences to being one or the other, although it can affect what kind of Fun activities your Sim prefers; Lazy Sims like to watch TV, while Active Sims will prefer physical Fun activities. Active Sims, however, will have an easier time progressing in a number of careers (laziness rarely being much of a virtue in the workplace), and will be able to more quickly improve their Body skill. Lazy Sims, on the other hand, have the aforementioned napping tendency, will sometimes miss work due to sleeping through their alarm (you can override this with manual control if you're attentive, though), and will tend towards the lower end of the Fitness scale.
In short, the only real drawback to being Active is that you'll require a bit more food than lazy Sims will, but this is relatively inconsequential compared to the numerous benefits that a high score in this trait gives you.
Serious/PlayfulThe Serious/Playful dichotomy is perhaps the only trait axis that is truly balanced between the extremes, in that it's usually better to be somewhere in the middle of the axis, rather than have your Sim be extremely Serious or too Playful for his own good.
Being Playful allows your Sim to acquire Creativity at a faster rate than Serious Sims, who in turn are better at boosting their powers of Logic. Their inquisitive nature encourages Playful Sims to seek out Fun in a variety of activities, but this need decays more quickly for them. Serious Sims get a bit of a boost in the Science, Law Enforcement, and Medical career tracks, but Playful Sims will have an edge when it comes to socializing, particularly when they have to deal with multiple Sims at the same time; being Playful allows a Sim to engage almost any similarly happy Sim in a wide variety of Fun activities.
Grouchy/NiceAlthough most of the trait dichotomies tend to give at least some small benefit to your Sim if you choose to emphasize the negative side of the continuum, it's just objectively better to be Nice than to be Grouchy. Unless you're a green puppet that lives in a trash can, no one finds surliness endearing, and the population of Simsville is no exception; Grouches are fantastic at self-sabotaging their relationships and generally annoying everyone around them to no end.
The benefits of being Nice are self-evident: Nice Sims are more likely to succeed with their social interactions, which in turn lets them more rapidly make friends, which is just obviously a desirable thing in a game like the Sims. Being a Grouch, on the other hand, will make your Sim less likely to accept positive socializations, and, if you leave them to their own devices, will actually result in all-around jerk-like behavior. A Grouchy Sim that's under the control of the AI will quickly manage to destroy any positive relationships that you've managed to work up; for an example of this, check the Pleasant family in Pleasantview and let the AI run Lilith for a bit. She has three points above being a complete grouch, but will still tend to initiate arguments and irritate the rest of her family, unless you are constantly override her commands. Having a Grouch in the family won't affect the rest of the family members' relationships with each other, but it will make it difficult to gain and keep the friendships that are required for career advancement.
Being Grouchy or Nice doesn't affect need decay, skill learning, or career advancement (aside from the previously mentioned difficulties in making friends), but it's still very difficult to have a Grouchy Sim be a success in life. On the other hand, if you're looking for a challenge, see if you can get a Grouchy Sim to the highest level of a career--it's harder than it will be for almost any other type of Sim.
(As a note, many of the more difficult social interactions, such as the various Proposals, are much easier to pull off if you have ten points in Nice. This isn't a requirement--you can still perform any of the interactions if you're willing to work a little harder on your Daily and Lifetime relationship scores--but can make things proceed much more quickly for Romantic or Family-oriented Sims, if you can afford the points.)