Nokia lumia 620 to sony experia
Sony should get already installed an app or function like Move my Data or Transfer Data or something like that. Enable that and follow instructions, it uses bluetooth on both phones after pairing them.
Elsewhere, the longest way is to export your Contact from you web account Hotmail.com in a .xml file and import them to your Experia web Gmail.com account, so phone later will sync data by internet, same as Lumias