They don't sound the same.
I find that the sizzle is more pronounced and obnoxious in the second clip, which is also the harshest sounding.
The third clip is lower in volume and it is darker too. Also, the bass sounds less controlled in the last chord.
I find clip one and four the most alike.
My guess is that the first clip is a Fractal, and the fourth is the analog amp. The first sounds less noisy. I could be fooled because it is the only clip without prenoise before the playing to prime the ear to be alert of the high pitched harsh noise.
It is hard to say what is the most accurate. If the amp is harsh, a slightly dull modeller might be preferable to some. If the amp is less harsh, some added harshness might be preferable to some. If the amp-cab pairing is floppy in the bass, a slightly thinner modeller may be preferable. If the amp is thin in the bass, a more floppy modeller may be preferable to some.
Personally, I find the AXE wonderful. And I have very little experience with the various modelled amps. So, since I can not judge it anyway, I don't care as much for accuracy as I do for inspiration and feel. And I do get a lot of that from the AXE FX3. At the moment, I mostly play the FAS models.