They're all great when they're properly restored, and any one can give you good performance. Any differences IMO are subtle, but I do have my opinions from having seen and repaired hundreds of them.
801's are the best designed b/w vectors, IMO. They're somewhat overengineered, but that was ok for their first attempt. Separate power board, separate heatsink for the bottlecap transistors, slightly more sophisticated circuits for various things, and a thicker metal frame. More parts, more cost, better made. They're tanks. And they tend not to burn up when they do fail (i.e., they fail more elegantly), whereas 802/v2000's will often torch strings of stuff on the deflection boards when they go.
Atari worked with Electrohome and WG to design all of their monitors, and they tweaked the designs with each successive model (801, 802, v2000). And they cheapened the designs at each stage to cut costs. They all get the job done, but both G05's are better constructed than the v2000 IMO. (801 > 802 > v2000).
And you can build a harness adapter to run an 801 in an 802/v2000 cab, and the difference of power supply is only a few volts, so it isn't an issue (which I've also tested ). However there are some issues with how the ground paths are run, that can cause waviness in some cases. (We had a separate thread about this a few months ago, I don't have a link handy). But you can make them work. But you're better off putting an 801 in an 801 cab, if it had one originally. V2000 and 802 can be swapped freely with each other (in cabs that came with either) as they're more functionally equivalent.
For 802 vs v2000, I'd take the 802. The deflection boards are much better manufactured, and the heatsinks on them are bolted on, not soldered on like the v2000. I've seen plenty of v2000's with the heatsinks (and transistor connections) loose and broken, just from being bent over. Whereas the 802 ones you can't break because they're wider, and they're attached with two screws, not solder tabs. I pad v2000 deflection boards more when I ship them, as the heatsinks make them more fragile. 802's are much more mechanically robust.
I also like the 802 HV cages better than the v2000's. The 802's used more supple wire for the anode, and the diode is mechanically isolated better from the anode wire, so wiggling the wire won't loosen up the diode, the way they do more easily on v2000's. The v2000 HV's are much more annoying to repair because of this, as the anode wires they used are very stiff, and they go right into the diode, so twisting the wire puts stress on the diode connections.
Again, the differences are subtle (and bordering on nitpicky), and any of them properly repaired will give a nice picture with a long lifespan, so I'm not really knocking the v2000. I just think the 802's are a little nicer built, and nicer to work on, versus the v2000's.