SQL Azure premium performance
As mentioned in the comments Azure SQL, shared or premium, differs significantly from on-premises considering the hardware and network infrastructure. This document compares SQL Server to SQL Databases (aka SQL Azure) and as commodity hardware is used on Azure it might explain the difference you experience: while a CPU stays the same on-prem and on the cloud the choice you made for disks in your on-prem might be different from the disk infrastructure in Azure SQL Databases.
I ignore the type of query you evaluated but in my experience and because of my scenario disk IOPS tend to be as much important (or even more) than the number of CPU cores and RAM, see limits.
Making it short there is no promise of equivalent performance between SQL Server and SQL Database considering CPU and RAMs only, even if these resources are reserved with the Premium option.
We have many Azure SQL Databases in production and few ones are Premium: we had great advantages in implementing telemetry to automatically gather information and being able to use it later as needed for analysis. Here is a link to the CAT blog post: http://blogs.msdn.com/b/windowsazure/archive/2013/06/28/telemetry-basics-and-troubleshooting.aspx
It does not apply specifically to Premium or to Shared but, If it fits in your project scope, you should take the effort to implement telemetry. Otherwise it is a good starting point to look for relevant queries to system views on Azure SQL.
If you want to achieve in Azure SQL the same performances you get on-premises I suggest to investigate and eventually optimize for the different scenario.