In other words, if one user is trying to find a block using staked coins and another using PoW, which one will find it and why? Will there be a fork in the blockchain in this scenario? If yes, then how does the network decide which chain to accept?
I have a fairly good understanding of proof-of-work, and am trying to understand proof-of-stake correctly as well.
In case of fork, according to whitepaper, the chain with highest consumed coin age wins:
The protocol for determining which competing block chain wins as main chain has been switched over to use consumed coin age. Here every transaction in a block contributes its consumed coin age to the score of the block. The block chain with highest total consumed coin age is chosen as main chain.
In actual implementation, sightly more complicated algorithm based on PoS difficulty is used:
PoS_block_trust = 2^256 / (target+1)
PoW_block_trust = 1
And the chain with highest total "trust" is preferred.
So, the answer to your question is: PoS block wins.
target=2^256 means any hash is acceptable, so the block will be mined almost instantly (both PoS and PoW), and the target will be readjusted very soon, so it's not of much concern anyway.