Last time I looked there was not a super capacitor as a drop in replacement. They need extra electronics to be used because of inrush current and over voltage protection.
They do not have near the storage time or capacity as a battery.
Agreed. For a start, look at something physically compatible such as
this (5.5V, 1.5F). Look at the associated datasheet for the maths. Sorting out the charging is easy enough. Regarding the backup (discharge) time for running the RP5C01 Amiga real time clock (I=15µA), you'll get 78 hours = 3.2 days backup time at best. By comparison, the standard 80mAHr Ni-MH battery will provide around 200 days or 6 to 7 months backup.
A lesser known fact about many super capacitors is that they can age rapidly. Read the datasheet mentioned above for details, but essentially this can be 3 to 4 years.
The rated lifetime of a Varta 3/V80H Ni-MH battery is around 6-7 years. So long as you replace the battery before it reaches end of life, there's a low risk of leakage issues.
