The B-1B is a low level conventional bomber at this stage, whereas the Blackjack (Tu160) is big enough to carry nuclear tipped cruise missiles

The B-1B can be fitted with a rotary launcher, for 12 ALCMs, by moving the bulkhead between forward and intermediate weapons bays. It is inspected, by Russians, every few years or so to ensure the bulkhead has not been moved. At the end of the Cold War, the plane became part of the START Treaty. The US made them conventional. Otherwise, they'd sit armed, on an alert pad, before the end of the Cold War.

The B-1B has hard points on the wings for carrying external launchers for air-to-air missiles and nuclear-capable ALCMs (4 on each wing), bringing the total to 20.

The B-1B has a low-radar cross-section and radar absorbent material on the outside of the aircraft. It can fly high, but its purpose was to fly fast and low, using terrain following software, below radar. It is capable of what the USAF calls "Global Reach, Global Power" -- able to reach its target and fly home.