Hey there! I'm going to give my own personal account of why I prefer TS4 as of now -- after being a strictly TS3 player for years.
I bought TS3 and TS4 in December of 2015.
I mainly played TS3 only! This was due to TS4's lack of features. Also, the crazy smiling problem...
..uh, yeah.
TS3 definitely has more to offer in terms of gameplay. When I say gameplay, I mean things for your Sims to do for activity.
HOWEVER!
In November 2018, nearly three years after I bought the game, Get Famous was released. This sort of drove my curiosity into giving TS4 a serious chance.
..And, well. I'll say this now: I can't go back to TS3.
This is coming from someone who used to swear up and down that TS4 was a highly watered down version of TS3 gameplay.
In a way, this is true.
What I realized about TS4 that now puts it above TS3 , is not in its gameplay -- its in the Sims.
They are very expressive! They aren't rigid in their emotions and motions -- one of my gripes with TS3. I'm not just talking about when their interaction animations play. I'm speaking of the details. When they're idle, walking.. even sleeping -- they give little clues to how they're feeling.
From the little mutters when they are upset, to the colorful ways they express excitement and the way they speak when they are sad -- it's amazingly well done.
It's something that I could never really find in TS3.
Even though TS4 may have less content than TS3 at the moment, the way the Sims react and express themselves -- through different emotions and facial expressions -- allows me to keep interest in the game's existing features. I just think the Sims in TS4 are much better done.
I should also point out that the way I experience TS4 Sims is not through the vanilla game. Boy, I couldn't actually do vanilla TS4 sims.. :D
I use Roburky's Meaningful Happiness mod, which heavily balances/smooths the emotions system, and More Personality Please! -- which not only enables all autonomous reactions for all sims, but eliminates idle chat..
..and eliminates the constant smile issue.
So, that's my two cents! If I were to sum the games up:
If you prefer diverse things to do with your Sims, then by all means go for TS3.
If you prefer focusing on Sims' personalities and their relationships/interactions with their family/friends, then by all means go for TS4.