It depends on the kind of work you're opting for. The basic difference between Azure Table Storage and CosmosDB is the Global distribution and Consistency levels.
In simple terms, Azure Storage table ain at high capacity in a single region, indexed with RK/PK and optimized storage pricing. On the other hand, CosmosDB aims for higher throughput by a multisecond latency, global distribution, automatic indexing of each attribute or property and SLA backed predictive performance.
CosmosDB is used for global distribution mainly, however, if that's not a factor to worry upon, Azure Storage Tables do the work.