The major difference between the two is that Analog is a virtual analog synthesizer and is subtractive, while Operator is primarily an FM synthesizer so the approaches to using them are fairly different. Analog tries to model the circuitry and characteristics of classic analog synthesizers, including their quirks. Operator is unashamedly digital, like many FM synthesizers. If you put an Ableton Spectrum object after Analog and Operator in turn (you can try this in the demo), you can see that Analog's sinewave generator has some subtle overtones in it, like I imagine analog hardware might, while Operator's is more "pure."
There are a few feature differences that might be important, too - Analog has two "channels" each containing an oscillator, filter, and LFO, however you can route between them a little bit before and after the filter section. Analog also has a formant filter as one of its filter types which Operator doesn't have. Operator, on the other hand, has only one LFO and filter, but it has four oscillators which can be either audible or used to modulate each others' frequency.
In general, Analog makes traditional older synthesizer noises, whereas Operator tends to sound a bit more modern. I personally think both are useful.
I'm not sure what exactly constitutes an industrial rock synth sound, but you definitely know the sound you're looking for - try searching through the presets for both Analog and Operator and seeing what their creators have come up with. Since you're using Ableton Live, check the "Instrument Rack" presets as well. Presets aren't the entire story, but they're usually a good way to get a quick feel for what a particular synth is capable of. There might even be a sound very like what you're looking for and if so, you've found your synth.