A broken antenna is not the most likely cause of poor data reception.
Cell phone signals are transmitted over several different frequency bands. Cell phone carriers are frequently shuffling these bands around and launching new frequency bands. As cell phones get older, the frequency bands that the cell carrier are using, and the frequency bands that your phone can support, become more and more mismatch. This results in poor reception of data.
The voice signal tends to remain on the same frequency bands.
When you buy a new phone, check if the phone supports all the frequency bands that your carrier is using and is planning to use. Just because it's a new phone does not guarantee it supports all the frequency bands.