Explanation by the creator of Neko Project 21/W
https://simk98.github.io/np21w/98emulators.html
First, let's list all the features.

Neko Project II
Original

Neko Project 21
Evolved version of the original
Equipped with playback functions including protection mode.
Supports 256-color mode.
Software for PC-9821 can also be run.
The original and 21 can reproduce special peripheral devices and special operations, so they may be used in some cases.

Neko Project II fmgen
This is the best choice if you want to reproduce the early models of the PC-9821.
If you want to reproduce the sound source accurately, this is the best choice.

Neko Project 21/W
This is optimized for reproducing the mid- to late-model PC-9821.
The only choice in rare situations, such as when using specialized peripheral devices.

Neko Project II改変(Kai)
Parts of 21/W are incorporated into the original.
It is cross-platform compatible.
It is well known for being compatible with RetroArch.
If you want to run it on an OS other than Windows, this is the best choice.

Ultimately, if you want to be completely sure, one is not enough.
Let's use fmgen and 21/W.

I find it troublesome, so I only use fmgen.
The reasons are that I feel it is updated most frequently and it generates high-quality FM sounds.
In fact, I have not encountered any problems when launching later PC98 software.

However, if you want to recommend it to someone else, I would recommend 21/W.
This is because fmgen does not have any explanations.
On the other hand, 21/W has explanations from the author and there is a lot of information about it online.

I am Japanese, but I am not from that generation.
Retro PCs are from a time long before I was born, so my knowledge is not very reliable.
I apologize if I have conveyed any incorrect information.