Little Big Planet is the best platformer game ever produced, Period. It's a really great concept... you have to reach from point A to point B just like a mario game.... but the main advantage is that you can virtually create anything to reach it. Also, the level creator mode is simply awesome.
The game is really awesome.
Note: It's not even remotely close to Sims in terms of concept. Sims is a different game whereas LBP is conceptually different. If you want something similar to Sims, then I would advice looking in other places. But LBP is one off the best games ever made... I haven't played civilization to comment on it, but reviews say it's a good game (score 8.5 on metacritics(average of more than 50 reviews)). LBP scored 9.5 on metacritics... So even the reviewers found LBP better.
Anyway, both are good games... Just go with which one you like more compelling to you.