DBMS follows the ACID properties of transactions, and BDMS guarantees them too. As a side note, since big data has too much data and too many updates done concurrently, maintenance of ACID properties leads to a significant slowdown of the system. In an ideal BDMS, it would have BASE (Basic Availability, Soft State, and Eventual Consistency) properties. 

Basic Availability refers to the fact that the system guarantees the availability of data when requested, and the data remains consistent in case of failure. The soft state of a system states that the system is consistent in case of all the states, like state without input, or the state with incorrect input sets. Eventual Consistency states that the system is consistent eventually, so a user is likely to get Twitter feeds once they are logged into their account but might not see them right away.