Identical SQL Server databases hosted in the same physical DB server
If these are quite large databases I would ask if they are on different physical disks, with one disk significantly slower or busier than the other? (i.e. one is SSD, and the other is a standard HDD).  

For smaller databases though, the data will quickly be cached, and so speed of the disk would stop being relevant at that point.

I'd suggest turning on Client Statistics and Show Actual Execution Plan to narrow down where the queries against the two databases are not aligned.