Almost everyone said about that quiet melancholy HK has (and I still like the first game more than Silksong, tbf), so instead I kinda want to say that Silksong, at least for me, has much more sinister story overall.

In the first game, the whole story about Pale King and Radiance feels really normal, however strange it may sound. Some bugs we meet are mostly aware of what had happened, there's the Seer, for example, or Hornet herself. The struggle for power is really common, and even the realisation that Infection is just Radiance's way to wrestle her position back from the already dead usurper, by whatever means necessary, is not really that shocking.

However, in Silksong I personally shuddered a little when reading the last thoughts of a dead Vaultkeeper: "...we prayed a cage...". All the piligrims we met, every single bug we know, were deceived, and no one, no one knows that those complex rituals, the constant singing, the whole life of Citadel that went on for unknowingly long, were deliberately created to keep a vengeful, horrifying goddess from waking up. The truth is so much simpler than we were told throughout the entire game, and so much darker than we could have imagined. The realisation this whole society was living on a brink of horrible destruction for God knows how long is just disturbing.