My favourite game from the Sims series is TS2. The second place is taken by TS3. I have played TS1 a couple of times (I was very young), but that game is very limited anyway when it is compared to other titles in the series.
Why do I like TS2 the most? I grew up playing it, but I can elaborate. Wants and fears which are determined by personality and aspirations are one of the main reasons why I love TS2. The sims in that game are able to have wishes and they are afraid of something at the same time. The sequels after TS2 do not have fears included which is unrealistic for a life simulator. The animations in this game are so livelike and detailed. There are so many group activities that can include more that 2 sims, which is necessary for a life simulator. The graphics of the game are beautiful besides the awful carboard look of the neighbouring houses and trees. The game overall is beautifully detailed. The game allows you to build anything (from curved bridges to skyscrapers). There is no limitation with TS2 besides the absence of a colour wheel which is in TS3. The player can litterally build a dome (it is not easy, but it is possible). I love how cc looks in TS2; the cc blends with the rest of the game. If you have certain lightning mods, the game will look even more beautiful. I have not even written anything about the expansion packs, but I will write less about them . OFB and Seasons are my favourite expansion packs. OFB allows you to create a business that sells literally anything. You can create a store that sells vintage cars if you want to (you do need cc though: there is no vintage cars in TS2)!
I do play TS4, but my game is heavily modded and I stopped buying the DLC. The game has the best character creator (if the colour wheel is forgotten), but the build mode is not the best becuase you are limited. The player cannot create skyscrapers, domes, curved bridges or apartments. There is also no colour wheel which was included in TS3. The maps are not 3D which is something that TS2 has (a game from 2004 is better than a game in 2014 in that regard). The player cannot create their own worlds which is something that even TS2 has. I do not like the graphics of TS4 because they look kind of lazily created to me: the objects are chunky, the hair is like clay, the ambience is ugly, the trees are not realistic enough, the skin is odly shiny, the textures are muddy and so on. Also, the sims have black cardboard instead of their eyelashes!
In my opinion, what differentiates The Sims 2 from its successors is the customization of the world. Even though you don't play in an open world (neither in TS4) you have the ability to customize every single aspect of the neighborhood: you can make your own terrain in SimCity4, you choose the land texture (green, desert, concrete but if you download custom content you can have alien-esque colorful lands!), you place the lots where you want and, with the help of the Lot Adjuster tool from Mootilda (she did so much for this community) you can put lots far from the streets and make a hermit shack or anything else that comes to your mind. You can create your own world, with its story and lore. And you can play the "Build a City Challenge" which, in my opinion, is so much fun because it exploits all the cool unique features of The Sims 2 that I listed above.
In The Sims 4 you are limited to those few, small neighborhoods that EA makes. They are so small that having large families becomes a bad idea, because if you want to separate the various branches of the family in multiple houses you basically occupy half a neighborhood and there's almost no space for other families! I think this is ridicolous... The Sims is a life-simulation game and what makes it unique from any other game franchise is the fact that you go on generation after generation, expanding your family's story. How can I play a family-oriented game if there's no space for the families to expand?
The Sims 3 allows players to make their own world but, come on, its difficulty is not absolutely comparable to The Sims 2. Creating a world in TS2 requires few clicks, it's a main feature of the game that has been there from the start; creating a world in TS3 requires you to learn how to use the CAW tool which is super complex, and it will take months before the world you work on becomes playable. I recognize that TS3's worlds are superior in the sense that they are massive, full of detail, you can explore every corner of them because it's one big open area. However, the effort required to create the neighborhood of your dreams, with the story that you have in mind, is unbearable for a casual player, so you end up using the EA worlds or downloading worlds from the internet.
Sorry for this long rant of mine. I hope my point is clear: TS2 is still being played because it allows you to make your own experience. Many of us don't care for San Myshuno or Sunset Valley, we want our own worlds.