I designed a backup circuit to allow graceful shutdown using an AVX 22mF BestCap capacitor. The circuit gave us enough up-time that it was used for years. The BestCap supply that we had is now depleted (obsolete) and I have been looking for an alternative. I found another 22mF supercap and tried it in the circuit but the output seems to switch off and then get unstable shortly after power is removed from the input.
Previously (with the BestCap) I got about 232ms feeding the downstream circuit after removing power, with the replacement it is 32ms and even then the discharge profile of the cap is wrong as it sharply falls off and then oscillates in a saw pattern.
I made no other changes to the circuit than replacing the cap (WV of BestCap is 4.5V, replacement cap WV is 5.5, but the circuit charges to 3.5V). The two caps, according to the datasheet, have comparable ESR (both list the max as 200mOhm).
Screen shot showing BestCap discharge:

Yellow trace is 28V input, blue trace is voltage of Supercap, pink is the 3.3V_PRIM which is the only remaining circuit after power removal.
After switching to potential replacement cap I get this:

Zooming in on the switch off point:

The only other differences worth noting is that the BestCap is soldered directly to the board... with the replacement I had to use 2 short (0.75" each) 24AWG wires to the pads. The BestCap was removed for the tests with the replacement.
This is the portion of the circuit in question:
