Differences between The Sims 3 for PC and PS3?

@RealSimmor0 You are correct, there are no expansion packs for the Sims 3 games on console. The Sims 3 and The Sims 3 Pets are separate, stand-alone games. You do not need the Sims 3 in order to play The Sims 3 Pets (my favorite of the two by far). There is no fixed or linear story progression in these games. Just like in Sims 3 PC and Sims 4, you can play them in any way you like. The Sims 3 Pets game has Mystery quests that I enjoyed very much, but they are strictly optional.

When you start a new game you have the option to create a new household in CAS or play an existing household. In this they are similar to Sims 3 PC and Sims 4. I think the maximum number of Sims per household is six but I never tried anything bigger than four. The CAS is close enough to the PC version of Sims 3 that I won't go over any of that here. The Sims have six life-stages, they will age (unless aging is disabled) and they can have children. Playable Sims can form relationships with NPC townie Sims and make them playable as well through marriage or asking them to join your household. The Sims 3 Pets game has dogs and cats (no horses) that are playable Sims. I don't think you can rotate between playing different families like you can on PC or on Sims 4 (at least not that I can remember). I think that once you pick a family in a new save you are limited to playing that family. 

Adult Sims have careers similar to the base game PC version. Children will go to school and teens will go to high school. You can create playable SimBots in Sims 3 Pets and there are Ghosts in both games, but there are no other occult types. There are full-time and part-time jobs and you can buy certain businesses. None of this is very different from the PC version, except for that the pets can have part-time jobs.

There are vacant houses that you can move into, both for starter homes and for upgrade homes as you gain Simoleons. I do not recall any completely empty lots in either game. The game allows for a small amount of Build/Buy modifications to the lots but there are limits. This is very limited compared to the PC version. Each lot has a type of empty vs. full "fill" meter and once that meter is showing completely full you cannot add anything further to that lot without first removing something else. The larger, more expensive lots in both games allow for more modifications than the smaller starter lots. Some of the public venues are rabbit holes (restaurants, schools, work places) but others are fully visit-able with complete interiors like the gym, the library, etc.

Both games have a game-play feature called Karma Powers that work similar to Whims and Reward Traits in Sims 4. As your Sim completes certain wishes they earn Karma points which may be exchanged for permanent buffs or one-time actions. Good karma powers include things like filling all needs or fixing/cleaning everything in the house. Bad Karma powers do things like curse another Sim (all their needs go to zero) or some really extreme things like turning another Sim into a ghost or dropping an asteroid on their head! Most of the Karma powers are either very useful or just for funny animations.

That's pretty much all I can think of. Of the two games, I preferred Sims 3 Pets for the better town, the cats and dogs (of course), and the Mystery Quests. The graphics, user interface, game controls, etc, are pretty much identical for both. You can still find a pretty good video review at IGN here if you like to see examples of all that:

https://www.ign.com/games/the-sims-3-pets

Good luck :D