The other way around is possible. You can install DIGITS app in your ATT work phone and get all your personal calls and texts in your ATT phone. All your texts will come to DIGITS app and hence wont be stored into the WORK phone Messaging app. All personal call will come to your work phone as well. Make sure to get your messages to DIGITS app in WORK phone, you have switched off the iMessage in your personal phone.
DIGITS is a T- Mo service which helps you to get all your calls and texts of your T- mo number to any connected device but not the other way round, Please let me know if you have any more questions.
In addition to what debjitjdv suggests, you could forward your work phone to your personal phone or get a dual-SIM phone and have access to both at once. If you shop for a dual SIM phone make sure that it has the bands needed to be compatible with both T-Mobile and AT&T.
OK, that's too bad.
I'll look into call forwarding and see what's up with text forwarding. Otherwise, two phones it is.