I have both consoles, plus I game on PC, and yes PS3 is by far the worst of all of them when it comes to voice chat.
Peoples voices sound like they're talking through a static radio, and you can hear all the crap that is going on in the background, as described in the OP.
And I've used numerous different headsets. I used the Sony brand headset that came out within the first year of the PS3's release. That was easily the worst headset I've ever used in my entire life of gaming. Then I've used two different turtle beach headsets, the sound from the game is fine, but when other people talk... it's god awful.
I use the same turtle beach on my Xbox 360 and while people may not sound exactly like they do in real life, at least their voice is very clear and clean.
Most PC games OR while using Skype, is crystal clear and easily the best voice chat I've ever experienced. And Xbox One uses the same system, and they've showed demo videos of it in action and it sounds amazing.