I opened this topic and it's clear it started in the TS4 section. I see people mentioning graphics, thats entirely personal. I love how the game looks, but the game does need a good computer to be able to play on highest settings (and lower settings are indeed ugly). When I started playing the game I played on medium settings which didn't look to well either, but I never minded back then. I don't play a game for looks. As for performance: same story. If you have a good computer, my experience is it runs as smoothly as Sims 4 for me (and that's with all packs installed).
So, that's looks and performance.
As for the game itself: Sims 3 is a game that becomes yours. It's big, it's creative, the sky's the limit where it comes to customization and there's so much to do and different ways to do it, that I can say that I still discover new things after nine years of playing (of which four years on a daily basis). The question is if you like that. Sims 3 is less scripted than Sims 4, the game doesn't take you by the hand to lead you through a script. And there is no way to tell if you'll like it. A lot of people love it, a lot of people don't. Let me put it this way, if I had missed Sims 3 in 2009 and I'd be in your shoes, the only correct answer to this question for me would have been: "Yes, buy it!" But it depends on what exactly you are missing in Sims 4 I guess. People adviced me in the past to at least try out Sims 2 (because I'd never played it when I bought Sims 3) because it was better. I've played that game now and for me that is not the case. I think we all have our favourite version and there's no telling what will be yours.
I disagree with "If you prefer focusing on Sims' personalities and their relationships/interactions with their family/friends, then by all means go for TS4" by the way. In my experience sims in 3 have more personality, because the game doesn't have the emotion system. Sims act more loyal to their traits and to the quality of their relationships and they take things very personal. If someone makes them angry, unlike Sims 4 they aren't angry with everybody, they are just angry with that one sim, and that can last a couple of days. I don't see that in Sims 4. It's true they behave less over the top than in Sims 4 and in a cartoony way I like that about Sims 4, but for me the more neutral sims in 3 work better, because I don't need the game to constantly show me strong emotions. Strangely enough those emotions lose their strength for me when they are constantly all over the place.