Why don't both black boxes hold the same data?
Black Box(s) is a misnomer, you have correctly mentioned their actual names.


  Why are the two black boxes holding separate data?


They have different purposes.

Flight data recorder: This is an electronic device employed to record any instructions sent to any electronic systems on an aircraft. It is a device used to record specific aircraft performance parameters.

Cockpit voice recorder: This device is used to record the audio environment in the flight deck of an aircraft for the purpose of investigation of accidents and incidents.


  Why don't black boxes hold copies of both the FDR and the CVR data for
  extra redundancy?


Since they record different data, they are different. They are built different.

Differences:

FDR


Time recorded: 25 hour continuous
Number of parameters: 5 - 300+


CVR


Time recorded: 30 min continuous, 2 hours for solid state digital units
Number of channels: 4


Similarities:


Impact tolerance: 3400 Gs /6.5ms
Fire resistance: 1100 deg C /30 min
Water pressure resistance: submerged 20,000 ft
Underwater locator beacon: 37.5 KHz
Battery: 6yr shelf life, 30 day operation
Both recorders are installed in the most crash survivable part of the aircraft, usually the tail section.
Each recorder is equipped with an Underwater Locator Beacon (ULB) or pinger to assist in locating in the event of an over water accident.



  Are there any technical reasons for why this isn't possible or hasn't
  been attempted yet?


It has certainly been attempted.




  Is there any benefit of having the CVR and FDR in separate boxes?


Probably the reason is that different teams investigate the data obtained from them as they have to recreate the scenario before the accident.

Regulatory Details


CVR: Due to the highly sensitive nature of the verbal communications inside the cockpit, Congress has required that the Safety Board not release any part of a CVR tape recording. Because of this sensitivity, a high degree of security is provided for the CVR tape and its transcript. The content and timing of release of the written transcript are strictly regulated.

FDR: Newly manufactured aircraft must monitor at least twenty eight important parameters such as time, altitude, airspeed, heading, and aircraft attitude. In addition, some FDRs can record the status of more than 300 other in-flight characteristics that can aid in the investigation. The items monitored can be anything from flap position to auto-pilot mode or even smoke alarms.