The Kursk was a different class of submarine....it was designed for launching cruise missiles as opposed to SLBM's (submarine launched ballistic missiles). Kursk was a big boat but much smaller than the Typhoon class.
Typhoons were basically designed to lurk under the polar ice cap and when the word came, to break through the ice and launch their 20 slbm's, each of which contained 10 warheads and could target 10 different populated areas (ie cities)....a total of 200 different cities could have been destroyed by each Typhoon submarine. Quite dramatic, no?
The caterpillar drive was basically a fantasy...although theoretically possible it has not been built, let alone used on any submarine in the world. In spite of that, the twin hulled Typhoon is the largest submarine ever built at about 575 feet long. The mock up used in the movie Red October was actually way too small and had elements of soviet Alfa submarines in its structure.