I'm not sure that, on the average, either is more or less reliable than the other. And as others have said, even in glass cockpits you're required to have an independent backup display. The avionics I fly/have the most experience with is the Proline 21 system (already mentioned by another poster), and I love it. Really good displays, and I've only ever had minor issues that were fixable while airborne. Others in my unit have had more serious issues, but we have a lot of additional stuff on the plane and fly them harder than they were ever meant to be flown, so it's expected. In all cases, through reversionary displays and the backup display, we've recovered just fine. It is very expensive, though.
Where there IS a very noticeable safety difference is the overall SA provided. For this reason, I'd argue that glass is safer simply because it's able to provide a lot of very good information simultaneously, in very easy to interpret formats. Most of it depends on what you pay for, but you can have moving maps, terrain readouts, real time weather, and other traffic all up at the same time, in addition to your basic altitude/airspeed/course etc. If you have the right package/subscriptions, you can pull up legal instrument approach plates and see your aircraft position transposed on top of them real time, giving you great SA/orientation with the field in the weather. Same with airfield diagrams on the ground. Overall, you're just capable of displaying a LOT more information. Though, again, it's going to reflect in your bank account.
And of course, like others have said, it's going to ultimately come down to training on whatever you go with and getting very comfortable with your displays.