I have an APX4000XH and can attest to the lack of information on its batteries. Short answer first, both the NNTN8750A and NNTN4321A work on the radio.
The battery originally specified for the radio was the NNTN8750A. They are very expensive if bought new and risky to buy used. The internal impres circuit places a small drain on the battery and if not periodically charged, they will kill them selves over time. Many of the used NNTN8750 batteries available on eBay may be no good if not stored a maintained properly.
The NNTN4321A is compatible with the APX4000XH, I have several and they work well. I’ve looked all over on line to find any information that says the NNTN4321A is a replacement for the NNTN8750, but never found anything. I only found one document that listed the NNTN4321A as an approved accessory for the APX4000XH.
The APX4000/XPR Mototrbo batteries are a totally different form factor and will not fit or work on an APX4000XH
I found this. It seems the NNTN8750 which is the battery that came with the radio discharges quicker vs the NNTN4321 battery. The two 4321 batteries both came fully charged with only 3 charge cycles on them. So it seems the 4321 battery is the way to go. The seller [Surplus Technology] has some NIB for anyone interested.
ACTIVE CIRCUITRY BATTERIES WITHOUT SLEEP MODE
The batteries listed below have a higher self discharge rate due to additional active circuitry required to meet specific regulatory requirements. For best performance these batteries should be charged and put into use within one (1) month of receipt. However, if storage is required, the batteries should be charged to a 100% charge state every 6 months.
ACTIVE CIRCUITRY BATTERY KIT NUMBERS
NNTN8570A NNTN8840 NNTN8750A NNTN8287 NNTN8386A NNTN8359A NNTN5510 NNTN7383
IMPRES Li-Ion 1250 mAh IECEx/ATEX IMPRES Li-Ion 2000 mAh IECEx/ATEX/M1 IMPRES Li-Ion 2050 mAh CSA
IMPRES Li-Ion 2300 mAh CSA
IMPRES Li-Ion 1800 mAh CSA IMPRES Li-ion 2075 mAh IECEx/ATEX Li-Ion 1420 mAh IECEx/ATEX
Li-Ion 750 mAh IECEx/ATEX
ACTIVE CIRCUITRY BATTERY STORAGE RECOMMENDATIONS
1. New batteries that will be stored should be charged to 100% state of charge within 1 month of receipt. Every 6 months, batteries must be recharged to 100% state of charge.
2. Batteries removed from service for storage should be charged to 100% state of charge. Every 6 months, batteries must be recharged to 100% state of charge.
3. Do not store batteries attached to radios or host devices. This will minimize current drain on the battery.
Note: Batteries removed from storage may take several charge / discharge cycles to achieve their optimal capacity. One or two reconditioning cycles will accelerate capacity recovery.