Are there any studies on the safety of glass versus steam instruments?
The FAA released a 70 page report back in 2003 titled General Aviation Technically Advanced Aircraft FAA – Industry Safety Study which basically says that the overall accident rate of the two types of airplanes are almost the same.  

They found that the "available safety" of Technically Advanced Aircraft (TAA) is greater than non-TAA aircraft, however in emergency situations pilots often were not aware of the resources available. To offset this, they recommend (among other things) more training for pilots before flying TAA's so that they actually have the safety related aspects available to them.

Here were their official findings:


  Team Findings: 
  
  
  The safety problems found in the accidents studied by the Team are  typical of problems that occurred after previous introductions of new 
  aircraft technology and all also reflect typical GA pilot judgment
  errors  found in analysis of non-TAA accidents 
  Previous safety problems similar to those identified in this Study have  been remedied through a combination of improved training and, in
  the  case of new aircraft capabilities, pilot screening (i.e.,
  additional insurance  company requirements of pilot experience). 
  The predominant TAA-system-specific finding is that the steps required to  call up information and program an approach in
  IFR-certified GPS  navigators are numerous, and during high workload
  situations they can  distract from the primary pilot duty of flying
  the aircraft. MFDs in the  accident aircraft did not appear to present
  a complexity problem. The  Team also believes that PFDs, while not
  installed in any of the accident  aircraft and just now becoming
  available in TAAs, similarly are not likely to  present a complexity
  problem. 
  TAAs provide increased “available safety”, i.e., a potential for increased  safety. However, to actually obtain this available safety,
  pilots must  receive additional training in the specific TAA systems
  in their aircraft that  will enable them to exploit the opportunities
  and operate within the  limitations inherent in their TAA systems. 
  The template for securing this increased safety exists from the  experiences with previous new technology introductions –the current 
  aircraft model-specific training and insurance requirements applicable
  to  high-performance single and multi engine small airplanes. However,
  the  existing training infrastructure currently is not able to provide
  the needed  training in TAAs. 
  Effective and feasible interventions have been identified, mostly  recommending improvements in training, and effective implementation 
  mechanisms for the recommended interventions exist. Therefore, TAA 
  safety problems can be addressed, and the additional available safety
  of  TAAs to address traditional causes of GA accidents can be realized
  as  well.
  


APOA has a nice summary here.