I was using my GoPhone card in my old 3GS just fine, and I had no trouble sending pictures. I then bought a 4Gm which required me to have my sim card cut in size so it would fit in the 4G. Everything has been working fine on it, but I can't send or receive pictures for some reason. I've tried changing my apn to wap.cingular and the PAYG one, but nothing works.
Why won't my iPhone send pictures? - 1
Because iphones are trash
Now you have to pay for data. Now, data counts as any multimedia now. The AT&T policies & stuff changed.
More than likely your new phone has already been updated to the new iOS 6. And your old phone was running on the old iOS. Since I updated my phone to the iOS 6 I have been unable to send or receive mms unless it is to another iPhone using iMessage. I have searched and searched for a solution to this and have been unable to find one. Seems some things work for some but not others. Good luck with yours.