Well, accuracy makes a big difference if you're trying to hit a hardened target like a missile silo. Missile guidance has been a constant effort to squeeze out more and more accuracy. Minuteman I started with an accuracy of 2 km, but now Minuteman III is said to have an accuracy of 120 meters. The Peacekeeper (MX) missile, no longer in service, is said to have an accuracy of 40 meters. You can use a much, much smaller warhead if you're 40 meters away compared to 2 kilometers.

The following was an interesting read on the super-fuze.

https://thebulletin.org/2017/03/how-us-nuclear-force-moderni...

One thing I never understood is why they phased out the peacemaker and not the much older minuteman.

The START II treaty limited Russia and the US's ICBMs to a single warhead each, and the Peacekeepers were optimised as a platform to host multiple independently targetable re-entry vehicles (MIRVs) and when the US agreed to revert to a single warhead per missile the Minuteman III was much cheaper to maintain than the Peacekeeper.

So even though Russia withdrew from START II almost immediately, the US continued to unilaterally remove the MIRV capability from its ICBM fleet and stick to single warhead Minuteman IIIs.

shooting something 12000 miles away, 0.1% off is 12 miles. That's missing the target and will not destroy whatever you were trying to destroy

In the early days, that’s why nukes went into the megaton range. Because then 12 miles will still destroy your target.

Then they got a lot more accurate than .1%

In general, the USSR had bigger bombs because they weren't as accurate as US bombs. So yes.