Yes, if you’re transferring your AT&T service, you should take your equipment with you to your new home. If you are an AT&T Internet customer, you will want to bring your AT&T Wi-Fi gateway, which functions as both a modem and a router.
If you are transferring your DIRECTV service, you should take your receivers, remotes, and owner's manual with you. When the technician arrives to set up your transferred service, he or she will take back what isn't needed. However, if you have a DIRECTV dish, leave it installed at your old address.