I disagree: If you summarize the difficulty of all Bitcoin blocks from the chain's tip and you're trying to "rebase" the chain at point x, you'd have to calculate at least the amount of hashes between x and the current tip to display a convincing fork with a similar cummulative difficulty.

In proof of stake, since there's no "work" that's connecting the blocks, but just a sortition of who gets to submit a block, this ever growing hash tree doesn't gain more difficulty over time to rebase.

That's what Bitcoin Maximalists always cry about and are never able to express in words.

Except only one of them requires ongoing capital investment which means you can't hold on to the return on your capital because you got it with practically no effort.

No.

PoS is a trust-based system. No different than fiat.

PoW is a work-based system. Similar to gold.

You can't have a free lunch. Sorry.

I am trying to learn.

In both cases, user A has to invest some amount of money.

In PoS, user A stakes money to make more money but gets penalized for breaking trust. Overall, user A makes say 10 coins over a 1000 staked coins ending up with 1010 coins.

In PoW, user A loses some money to make more money. User spends 3 coins to make 13 coins, so user ends up with 1010 coins

I don't see the difference yet.

I think the more interesting part is investment into a bad behavior. And that's what most PoS are trying to solve, ex. with slashing, etc.

With PoW regardless outcome you have to spend money on "work", to buy IRL electricity. And even if you fail with your attack, say 51%-attack, it still costs you some significant amount. With a _naive_ PoS you revert your attack costs on chain, i.e. you can do as many attacks as you want, you can do them even in parallel and it's going to cost you few bucks maybe of computer time.