If I may pop in, I've been looking into this crazy problem off and on - it seems to be an ongoing thing with The Sims 3...
In 2011, I saw threads of people saying it would only record a Black/Blank Screen. Then, people were able to record but since 2013 some were getting 'darker than it looked while playing and recording' output. It wasn't just Bandicam, it was happening with Dxtory, Xsplit's Gamecaster, Fraps and then NVIDIA's Shadowplay - all gave 'slightly darker' recordings, for many people. So odd.
I myself am getting slightly-dark video recordings from Sims3, but I wasn't too concerned about it, as it wasn't any recordings I was sharing and I wasn't really recording it much - but I still glanced at the problem once in a while on the net and kept track if anyone had any 'real' fix for it - which noone seems to have for those having the problem... all the threads talking about it just trailed off and noone came back on forums at NVIDIA, YahooAnswers, etc.
[I just tried recording it again with Bandicam and MSI's Afterburner and yep, the problem is still there.]
What an odd issue and I'm sorry that you are running into it now... I shall try to work on it a bit, changing settings and system configurations, to see if I can figure anything out - it would be great to find out what's wrong and I would share it here. It seems though, that either you are getting this issue or you aren't, and if you are, there's no real 'fix' for it [that I have come across so far]... crazy