I am an aircraft avionics engineer and have seen heaps of intruments both air and electric. Our workshop has a gyro overhaul section in which I have overhauled many gyros. Here is what I have noticed.
Note I am only talking gyro instruments here.
Usually a gyro instrument has failed because one or more of its bearings have failed.
In air intruments the number one cause for failure is bearing contamination due to a dirty air supply. Piper chieftan's have a pressure air system. When the pump fails it pushes bits of carbon into all the gyro instruments. 9 times out of 10 if this happens all the gyro instruments will need to be overhauled. I have lost count of how many times this has happened to a customers plane. We tell them to clean the lines and filters. We then overhaul the instruments, send them back where they refit them. A month later we get all the gyros back with a request for repair under warranty. After inspecting the instruments we see they have been contaminated with carbon. After talking to the customer we find they did not clean the lines because they thought it would take too long.
The number 2 cause of failure is handling damage.
Gyroscopic instruments have very high quality bearings in them. They also have a lot of weight hanginging off these bearings. A small knock can dent the bearings to the point the intrument will not operate correctly.
One of the gyro manuals states that if you place a gyro instrument on a hard surface then pick up one end 1/2 and inch off the surface and let it go. The impact will damage all the bearings to the point the instument must not be used till all the bearings have been replace. We never place a gyroscopic instrument on a bench without sitting it on a piece of foam.
So for everyone with air gyros make sure the air supply is clean. This means having good filters.
If you remove your instrument be very careful with it. A firm knock against the dash when installing it can damage the bearings.
For electric gyros the same conditions for handling care exist.
For the most part the electric side of things is very reliable.
Which one is more reliable???
I would say that electric is more reliable. Having said that if you can be sure the air supply is good an air driven gyro will last a very long time.
My boss has an RV-6. He used electric gyro's in his plane.
As far as other instruments such as mechanical airspeed and altimeters etc.
I would say the airspeed indicator is the most reliable instrument in the average aircraft. I have never seen one fail.