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:
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
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
APOA has a nice summary here.