Peercoin proof-of-stake: When a person with large computing power and a person with a large stake both compete to generate a new block who wins? 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.