Preface: The question seams to ask for opinions, as it is opinion if someone accepts an emulation, no matter if software on a CPU or on a FPGA, as the same as the real thing or not.
Ask yourself, is driving a modern technology car pimped up to look like an SSK the same as driving the real thing? Do you want to ride a 1950s BMW with all it's sounds, smells and vibrations (and all the tinkering needed to keep it going) or a 2020 electric bike made to look like one, giving you the classic sound from a build in iPod?
I'm wandering what are the differences between using a real hardware, FPGA based hardware emulators like MiSTer and the large amount of software emulators for different systems running on modern Windows, MacOS and Linux computers.
If you're just a user, convinced with using your modern keyboard and modern mouse handling some image, that looks like 640 x 400, on your 4k screen, then software is all you need. Already a FPGA version will be overkill, as it uses the same modern devices.
On the other hand, if imaging is not enough, but you want to feel the bulky Atari mouse, the wiggly Amiga keyboard or the bulky C64 joystick, all presented with real CRT glare, then there is no other way than getting the real thing.
One thing which came to my mind is that both software and hardware emulators could be not precise enough
By now they are. in each and every detail. Modern hardware isfast enough to allow the use of HLL software to aquire cycle exact timing. Especially when all in and output is emulated anyway, mapped to modern devices.
But this seems to me like something depending on the quality of the implementation which can vary between different emulators and improve over time because of bug fixing, but not as a fundamental issue.
Lazy programming and maintenance doesn't invalidate the approach. For all purpose, except real hands on hardware, there is no difference.
Also I'm hearing about the latency issue with the software emulators, but I'm a little surprised that something like this can really be felt on a computer which is probably millions time faster than the emulated machine.
Maybe a hundred times, if at all. Keep in mind, most major components haven't gotten as much faster - and most of that has been eaten up by larger size devices and data needs.
The Latency issue is something that has been around since like always. There will be always some stating they can see/feel the difference. While this may be true in a few, very dedicatied situations it's rubbish most of the time. Claiming feeling a few microseconds, when testing a joystick already may cost more is simply fantasy.
Is there really a technical reason to prefer real hardware or FPGA based emulation vs. software emulation
What constitutes a technical reason for you? In itself the term is not clear when comparing complete different implementations.
or this is just a nostalgia thing, caused by desire to fill like you are really back in the 80's or 90's?
Have you ever sat in front of one of the old machines? It's surprising how different keyboards feel when leaving today's standardized equipment.
And then there is of course the hardware tinkering - not real fun with emulators, as here adding an interface is merely adding a few lines of code - or just configuration in some cases. No layout, not etching, no soldering and especially no cursing and patching until it works.