In terms of track circuit reliability, the track circuit equipment itself is often very reliable (except the ASTER / SF15 types which are obsolete and hence there is a lack of spares). A significant number of track circuit failures are either cable problems or just as, if not more likely, problems with the track.
For a track circuit to work correctly and be reliable, the ballast has to be in good condition (no muddy wet beds), if concrete or steel sleepers are in use, the insulations for the chairs (pads and "biscuits") need to be in good condition, the Insulated Rail Joints (IRJs) need to be in good condition, and if point work is involved, the insulations for all the stretchers and point operating equipment needs to be in good condition.
Unfortunately, poor or a lack of proper preventative maintenance means that many of these get left until a failure occurs...
It's really difficult to compare track circuits to axle counters in terms of reliability and the reasons for why the failures occur, because they are completely different systems and work very differently.
Under BR, Western Region at one time found some money to fund a programme to improve track circuit reliability. This worked very well. Most importantly, because old cables, connections were renewed with a better rail fixing method plus "doubling up" the cables to the rails (two independent cables, so if one was damaged, the second would allow the track circuit to continue to operate normally). But also because other defects were reported and fixed.
Poor ballast / track conditions can cause axle counters to fail. The rail mounted head can fall off the rail if the vibration causes the nuts and bolts to work loose.
Being far more complex, means the electronics that form a large part of the axle counter system can fail in many more ways compared to conventional track circuit equipment. One single equipment failure can cause two or many axle counter sections to fail.
So, I hope I have given you a flavour of the differences. And why (apart from simple statistics), it's not easy to say which is better overall...