The equivalent match on the western side was the B-1, which was built earlier and served a roughly similar role until it was mostly replaced by the B-2 and now both are being retired in favour or the upcoming B-21.
The B-1B was not an equivalent to the Tu-160. One could go above Mach 2, the other could barely go above Mach 1. The B-1A would have been a match if it wasn't a failure.
By your premise any plane that flies even 10% slower doesn't match up, even if it's superior in every other way.
You don't have to match exact speeds to match outcomes when it comes to bombing. What matters is what the platform is meant to achieve and how effective is it at its mission. A slower supersonic plane may be the superior overall platform, depending on the other aspects of the plane.
Russia made a hyper expensive show pony, when they could have built a cheaper, more effective platform at a lower speed. That's usually the kind of mistake the Americans make. The relatively high max speed of the TU-160 turned out to be entirely meaningless, they would have been better off building a different plane.
The TU-160 has a $200m+ price tag. That's $1.2b scaled to the US economic terms. It's something beyond hyper expensive for the Russians in relation to their economic capabilities and military spending.
The B-1A was cancelled. The TU-160 should have been cancelled.
