Bitcoin uses Proof of Work (PoW) to secure its blockchain and prevent double spending. PoW protocols deliberately “waste” electricity to make it economically and physically impossible to attack the chain.
Newer coins such as PIVX use Proof of Stake (PoS) to secure their chains – this is good because it does not “waste” electricity but it allows costless attacks. Therefore the only security is the efficiency of the code. This is a concern when state actors with huge computing power and massive human resources could decide to attack a chain.
Evangelos Deirmentzogloue gives a good introduction to attacks on PoS in this Medium post.