Problem with Restored DB
Firstly as @jonhg points out the servers can give you different execution plans as the tables and indexes are rebuilt. The server hardware (memory, cpu, hard drives) can be different and finally you don't have the same version of SQL server in both cases. Any of these would be sufficient to give different results. 

Other queries could be interfering, as the cache on the servers can be different. All the answers to this are found here: http://download.red-gate.com/ebooks/SQL/eBOOK_SQLServerExecutionPlans_2Ed_G_Fritchey.pdf