Passive is what you get in the theater, period, but it bears no resemblance to the passive used in home TVs by LG. They have almost nothing to do with one another, to be honest.
The theater passive is a different enough technology from either the active or passive in-home technologies.
To say in-home active is "more advanced" is kind of nonsensical. (The reason RealD isn't in your home is because it's too expensive to implement; it's quite a bit more advanced than what's in your TV in many ways.) Theater 3-D is much more forgiving with respect to head movement and location in the room. A lot of active home systems suffer from some or a lot of "crosstalk" which is a huge negative.
Then there are passive home system's like LG, which cut resolution a ton (bad), but offer a powerful depth illusion (good).
It's fair to say there are tradeoffs all around and people will have their own preferences.
There is no difference in HDMI cables. If you can see the picture without visible dropouts or sparklies, the cable is working at 100%. No other cable will display a better version of that picture. You're simply wrong if you think there is a better digital cable than one that is already working.