The Soviets, at that time, planned to use bombers on one-way attacks, doubling their range.
To be fair, most American planners did not expect the vast majority of aircrew to return to the United States, either. Badger, Bear, and Bison bombers would be the primary threat to the United States. The Bear is probably the most capable Soviet bomber -- it certainly has the longest range, but I imagine that regardless of the range of the bomber, most of the work is going to be done by missiles.
My thoughts go along the lines of a 10% success rate for the 200 Soviet bombers, 15-20% for NATO bombers, and 75-80% for both sides' land-based missiles. At sea is the greatest disparity, with only 5% of Soviet sea-based missiles hitting targets, and 75-80% of American sea-based missiles.
The difference at sea is due to the vast difference in missile and launching style. Soviet submarines have to surface within radar range of the American coast in order to launch their missiles. In addition, they must wait on the surface as the missiles' gyroscopes spin up. One can only imagine the tension during those 20 minutes between surfacing and launch. That's why I envision only a 5% success rate -- not only do the Soviets have to run an established ASW gauntlet, but they've got to survive surfacing and the time needed to launch their missiles. I predict that their only successes will come in the Pacific, where the deeper waters and wider area minimize Soviet disadvantages. Guam, Pearl Harbor, Okinawa, and likely many of the other island outposts can be hit -- with difficulty, but much less so than the continental cost.
American sub-based missiles, however, are a generation more advanced. The Polaris A-2, carried by most of the US's submarines at the time of the Crisis, can be launched underwater, doesn't require the submarine to expose itself, and can be 2700km (1500nm) from its target. That's roughly ten times the range of the missiles Soviet submarines are carrying.