Good morning Nandan,
On Azure SQL database all your queries and processes should be well optimzed. Examine the query plans.
Some service tiers limit the max degree of parallelism that queries can use , in some workload scenarios like this one that can benefit performance but in others that can hinder performance.
On Azure SQL the benefits of maintaining indexes and statistics is crucial for performance. Use Ola Hallengren scripts to defrag and update statistics and then test performance again.
In addition, premium tiers use local attached SSD which faster is. Examine what kind of waits you are seeing when those processes execute. If you see IO waits, then Premium tiers should be considered if indexes and statistics are in good shape.
In terms of CPU resources premium tiers do not mean more advantage, for example a P1 tier has a max degree of parallelism of 1 core. While a S12 tier has a limit of 22 cores.
Depending of how the workload is intensive on IO or CPU you need to take that in consideration when hardware sizing your project.
RAM memory is another important factor, for example a P1 is limited to 5 GB of RAM (5610496) despite been a Premium tier.
Finally, make sure you have no important missing indexes if you are using Azure SQL, or you may have to scale up resources to get the performance you need.
We are here to help you. You can contact me personally if that speed up things for you.