Pictures and videos are stored on the SD card in the HTC Thunderbolt not the SIM card. The text messages need to be backed up to the SD card using one of the several SMS Backup applications in the Play Store.
Does the DROID Mini have a SD card slot in addition to the SIM card slot needed for the phone to connect to the network? If there is a SD card slot, you can simply move the SD card from one phone to the other. If not, you need to utilize a computer to transfer the files between both phones.
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It's important to transfer your information to your new phone! Your SD Card stores your music, pictures, and videos. Your Sim Card does not store any information except V-Cards. You should be able to move the SD Card from the Thunderbolt to the Droid Mini. Keep me posted.
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