Hello,

Thought to share about some concepts widely used but never really made a effort to learn in much detail until today. I have simplified the concepts as much possible so its easily comprehensible to any newbie as myself. If I  have missed out or wrongly stated anything please let me know. Hope its useful!

The concepts of Proof of work & Proof of stake have risen due to the consensus mechanism inherent in blockchain technology. Consensus mechanism is the process of collectively agreeing on the content to be added to a distributed ledger which is also more commonly known as a blockchain. The purpose of the consensus mechanism is to ensure the validity of information added, this in turn in prevents double spending in the case of a currency, or invalid data being added to the block chain.
There are several consensus mechanisms but for purpose of this article I would contrast the currently most discussed methods, which is Proof of work (PoW) and Proof of stake( PoS).

Proof of work
Bitcoin utilizes a proof of work (PoW) system and works in the following manner,
1. A set of transaction is bundled into a memory pool (mempool)
2. Miners verify each transaction in the memory pool by solving a mathematical puzzle
3. The first miner to solve the puzzle is awarded with newly mined bitcoin also knows as block reward
4.The verified mempool now addressed as block is attached to the block chain.

Proof of Stake
Under this method there is no need to solve a mathematical puzzle instead, a creator of new block is chosen based on their stake. Stake is the number of coins/tokens one possesses. Under this system all tokens/coins have been already created so there is no block reward instead the miners would get a transaction fee

Differences between proof of work (PoW) VS proof of stake (PoW)

Cost and Engery
PoW – Very energy intensive as it requires very high computational power which is required to solve complex mathematical computations

PoS – Fraction of the energy is required compared to that of PoW and is considered as the greener and more environmentally friendlier consensus mechanism. Due to the low energy and low cost the PoS has becomes more dispersed as opposed to PoW where mining has been increasingly reserved for large scale operations.

Security
PoW – Forking of blockchain is not desired as it is unhealthy for a network and can lead to instability. Under PoW system if a blockchain is forked miners will have to chose between the blockchains or if they plan to support both blockchains their computational power has to be split. As a result from an economic perspective forking is generally discouraged under a PoW system

PoS – This system does not inherently discourage forking and therefore when the blockchain is forked it can possibly result in a problem knows as “nothing at stake”. This essentially happens when a validator/miner receives a duplicate copy of their stake for a newly forked blockchain and he is able to sign off on both forks and potentially claim twice the amount of transaction fees as a reward and double spend their coins. A participant is not required to increase his/her stake to validate transactions on multiple blockchains and results in no economic incentive preventing the nothing of stake problem in the PoS system. A potential future solution to this issue is the introduction of a deposit system that would be introduced by Vitalik Beauterin in his proposed proof of stake consensus protocol named Casper which is a expected to be implemented for Ethereum in future possibly in 2018.

Centralization
PoW – High risk of centralization mainly due to the reason mining being a expensive process and therefore reserved predominantly for large scale operations. This is contrary to the main principle advocated by blockchain technology which is the concept of decentralization

PoS – A fairer concept in which the amount of network control granted is directly proportional to the the amount invested in the token/coin.