What is the kind of attack that was prevented by switching BTC code from "the longest chain" rule to "the heaviest" one?

As you most probably know, in version 0.3.3 of the BTC core there was introduced a significant update where the "longest chain" rule was replaces by "the heaviest chain" (the announcement https://satoshi.nakamotoinstitute.org/posts/bitcointalk/268/, the code lines https://github.com/bitcoin/bitcoin/commit/3b7cd5d89a226426df9c723d1f9ddfe08b7d1def#diff-608d8de3fba954c50110b6d7386988f27295de845e9d7174e40095ba5efcf1bbR1236).

What I can't really get is what's the attack scenario it should have been preventing, which could allow a "less than 50%" attacker abuse the disadvantage of the "longest chain" rule compared to the "heaviest chain", taking into account that in the same difficulty adjustment epoch the "longest" and the "heaviest" means the same (if I'm not wrong about how the heaviness is calculated - via the accumulated work defined by the difficulty thresholds of every block in the past of the given one plus its own difficulty) and it could only probably differ at a moment of difficulty adjustment?

The only attack scenario I can think of is attacker mining for a really long time, waiting for his local difficulty to drop so much that he alone could mine at a rate of 1 block in 10 minutes, and then hoping for the main net to hit the unlucky strike of a line of slow discovered blocks, while he in the same time is lucky enough to mine more blocks to a) compensate his initial waiting for the difficulty drop when he had been finding blocks much rarer than 1 in 10m (since he was only a part of the net then) plus b) manage to also overtake the other part of the net.

Can somebody explain this to me?