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.

Privileged take. You probably get paid in or have access to the USD or EUR.

Consider majority of the world doesn't.

https://bitcoinmagazine.com/culture/check-your-financial-pri...

If you have the means to access bitcoin, and can withstand the radical swings in exchange rate, you are already privileged.

What privilege? Can't you be more explicit?

I mean, I think they were pretty clear: the privilege of having ready access to/being paid in USD or EUR.

(I don't particularly endorse their view, but I did think their statement was clear enough.)

I don't see how having access/being paid in USD or EUR is a "privilege", or the connection this supposed privilege has with crypto-currencies.

They were pretty clear - the privilege of having direct access to USD or EUR.