Bitcoin, Ethereum, and other successful cryptocurrencies are backed by open source code that defines a controlled money supply, distributed via proof-of-work or proof-of-stake, to the nodes that support the network.  They represent digital scarcity that is controlled by code, not by people. The current Petro is a token on NEM with the supply entirely controlled by the Venezuelan government.  There is a promise to move to it's own blockchain, but there are no details available about that blockchain.

If you like the Maduro dictatorship and believe their promises, I recommend you buy as much Petro as you can possibly afford.  Then, I suggest you save up and buy as much of their gold "backed" coin as you can as well.  You will get the same reward as all Venezuelans have - both Chavista and opposition.

I can't imagine why anyone would invest in the Petro unless it's to make some pro-Maduro political statement.  There are too many good opportunities out there.  Problems with this coin include:

(1) The Maduro regime says the Petro "backed by oil" and that claim is being repeated by those following the story, but there is no official communication on how that backing works.  There seems to be a perception that one Petro will be equal to one barrel of crude oil, but I can't find anything from the Venezuelan government that explicitly makes that commitment.  In fact, there is a formula in the white paper for the redemption value in Bolivares and that equation has a "Dv" discount factor that is set by the Venezuelan government.  In other words, they set the value of the Petro.  To actually back the Petro in oil it must be directly redeemable.  Not necessarily by individual investors, but as an example - if China were buying 1mm barrels of crude oil from Venezuela and paying in Petros, the price should be 1mm Petros.  There is no document that makes that commitment.

(2) Even if the Maduro regime made a commitment to redeem the Petro for oil, who would hold them accountable?  Their typical pattern would be to start off with a commitment like that and then declare some sort of emergency or economic warfare that means they need to devalue the coin.  No matter what you think about the politics and the truth behind those stories, the fact of the matter will be that the Petro gets devalued and investors lose money.

(3) The idea is that the Petro will be issued on its own blockchain, but that blockchain does not yet exist and there are no technical details available about its design.  What is being sold now is a token on another blockchain.  (See my next point for the problems with that.) What we do know from the white paper is that it won't be mineable - the government issues all the coins.  They say that the supply will be capped, but until they show us code that locks them in to a fixed supply there is no reason to believe that.  Also, if it is not mineable and it will only allow for proof-of-stake at the discretion of the Venezuelan government, what will be the incentive to run nodes?  If the Petro can't attract a critical mass of independent node operators around the globe then it won't be a true decentralized cryptocurrency.

(4) The Petro website and white paper both specifically said that the token would be issued on the Ethereum blockchain.  Then, the day of the resale it was announced that it would instead be on the NEM blockchain.  At that point the white paper and website still said Ethereum.  (They have now updated things.)  I'm no expert on the technology, but going from one blockchain to another for your tokens is not something you just switch last-minute.  The NEM plan was in place for some time in advance for reasons unknown and unexplained.  It's a clear example of the lack of transparency around this cryptocurrency.

(5) This coin is brought to you by the same team that manages the Bolivar which has collapsed in value.  You can debate whose fault that is all you want, but the fact of the matter is that if you have been holding Bolivars for the past few years your investment is now near-worthless.  Since the Petro is not really backed by hard assets and the regime has explicitly stated that they will set it's value (in the white paper) there is no reason to think that its value will hold any better.  For more of my thoughts on the Maduro regime's money management skills, see:

http://bair.com/2018/02/12/the-venezuelan-bolivar-one-reason-im-a-crypto-believer/

I do think that one bit of good may come from this crypto-scam.  Now non-Venezuelans who believe in the Maduro regime can invest in the Petro and experience a little bit of what Venezuelans have suffered for many years.  When people start losing their money, it may start to change some minds.
 
I obviously have some strong opinions on this given that my wife is from Venezuela.  But, no matter which side of the politics you are on I can't see a rational reason to invest in this coin.  There are many options that are truly decentralized, transparent, and proven.