You can sent most pics from most nokia phones as text messages using the SEND VIA MULTIMEDIA function on the phone...
You don't say what the new phone is tho

I know my one (6230) has a seperate MMC card in it - the phone stores the pics to the phone mem (as will all, it don't go to the SIM) and I copy em to the MMC card then take it out, plug it in my card reader on PC and upload em to a folder on PC. To send em to another phone that is picture enabled I just send either via blue tooth or multimedia text