Make Arduino send and receive at the same time
I am using SoftwareSerial for both.


As others have said, you cannot listen to 2 SoftwareSerial ports at the same time.


  Should/can I use HardwareSerial and SoftwareSerial?
  
  ... can the Arduino receive from GPRS and GPS module data at the same time? 


Yes, but...

This answer provides full details on choosing "good" combinations of hardware and software serial ports.  To summarize:


Use the HardwareSerial port (i.e., Serial) for one of the devices.  You can still use it for debug prints, as long as the device has some kind of command "format".  For example, if commands start with "AT", just make sure that none of your debug prints start with "AT".  It is the absolute best choice.  You would have to disconnect RX pin 0 from the device in order to upload new sketches over USB.
Use AltSoftSerial for the other device.  It is the most efficient software serial port, and it can be used at the same time as Serial.  It only works on two specific pins.
NeoSWSerial is the next best choice, at limited baud rates.  It can be used with the above choices, but transmitting on NeoSWSerial prevents them from receiving.
SoftwareSerial is the worst choice.  Receiving or transmitting on SoftwareSerial prevents all of the above from receiving anything.  It disables interrupts for long periods of time.