Stored Procedure Execution - Takes much more time in One Server comparing another Server

Server 1 and 2 - Sharing same Specs and Configurations. SQL Server Edition is also same.

am trying to Execute a SP : with same set of Project and No of Rows used in all Transaction tables are same.
Server1 - Takes 1 Second
Server 2 - Takes 4 minutes 40 Seconds.

Only difference is Server 1 total DB size is 45 GB
Server 2 is 120 GB.

But still the SP execution is not dealing with any common table - Its all with Individual Tables for each Client. Any one suggest a solution to fix this.

have you looked at execution plan for each proc?