Vetinari goes to Westeros.

[Crossroads Inc.]

I can only imagine if the set up was altered slightly so that BOTH Vimes AND Vetinari were moved over, how much their dynamic together would change things.

After all, Vetinari in his own way created the Vimes we know today, and in fact says as much to Drumknott.

One thing to remember.
Vetinari on his own can perhaps create a new spy network as well as support structure.
But Vimes... Well... He has FAMILY.

Sybil and Vimes Jr,
In "Night Watch" he all but abandoned the future, except for the thought of Sybil and a baby to be.
If he was once more ripped from his family, never to return. Well, that could very well break a man like Vimes, driving him back to the bottle.

[The Romulan Republic]

I don't know. Maybe.

But I feel like even if he went much darker, his commitment to Justice is too strong at this point to simply curl up and drink himself into oblivion in an alley again.

Besides, if it were him and Vetinari together (which was scenario three in the OP), I'm sure the Patrician would be doing what he could to prod and motivate him to action.

[madd0ct0r]

How would we even start to figure out how quickly Vetenari could build up his spynetwork? By it's very nature, it's not something there's much infomation on.

Ugh...

Maybe assume each informant requires 1 gold piece per unit time, giving a max number of spys for an income? Assume each one can only recruit 1-2 others per month? BUT the thing is I just see him plugging into the existing spy networks, so for everyone below the subverted node, they continue buisness as usual, so the recruit 1-2 people per month would be the upper limit on time, with effective spies being more effeceint?

[Simon_Jester]

Vetinari has immediate access to Tywin's spy network, which is a very good place to start. Furthermore, he has Tywin's fortune, which is large but not unlimited- in canon, the Lannisters were basically able to keep Robert's treasury afloat despite massive graft causing the tax revenues to fall apart, because they could afford to loan him money.

Vetinari can take that money and use it in other ways.

Furthermore, he has no fundamental reason not to make deals with Varys, who has the only other spy network of real value in King's Landing.

[Titan Uranus]

In canon, I'm pretty sure that Littlefinger has a spy net superior to Tywin but inferior to Varys in King's Landing.
The problem with this crossover is that Vetenari and Vimes (to a much lesser extent [Knurd]) are supernaturally competent. However, discworld being the way it is, it's not clear whether they are supernaturally competent because of the magic of the disc or if their abilities would translate to Westeros.

For instance, Vetenari can cannonically turn invisible with some (definitely limited) preparation. This is not presented as magic in the discworld setting, but it's also not possible without magic in Westeros.

[The Romulan Republic]

I'm going to assume, for the purposes of this scenario, that Vimes and Vetinari are simply very skilled and strong-willed but ultimately non-magical humans.

[Titan Uranus]

I'm going to assume, for the purposes of this scenario, that Vimes and Vetinari are simply very skilled and strong-willed but ultimately non-magical humans.

But especially for Vimes, their supernatural abilities are an intrensic part of their character.

What is Vimes like if he is not Knurd?

Because he certainly isn't post Guards! Guards! Vimes. Nor is he necessarily Drunk and Beaten Vimes.

[The Romulan Republic]

Hmm... Its a difficult question.

I'll say, then, that any abilities they have which affect only themselves, like Vimes' "inner watchman" or this Vetinari invisibility thing, are in effect; but any that would affect other people/objects directly, like, say, Narativium warping events to fit the story, or extraordinary charisma/persuasiveness beyond mere human ability (something I can see Vetinari having, at least), are not.

That seems fair, doesn't it?

Edited to fix typo.

[Titan Uranus]

In that case, Vetinari is better at spy-work and managing a spy-net than Varys, better at finance than Littlefinger, more politically adept than all the high lords of Westeros put together, understands the concept of investment, probably better than the Iron Bank, and is better at murdering people than the faceless men (or at least he is on the same level). And you just gave him the best hand in Westeros.
The only problem is that Vetenari is guided by his patriotism, I'm not sure what he would strive for without his beloved city.
But assuming he works for the welfare of the people of Westeros, I think he would contrive some way for Arys to die and for Raegar to get the Iron Throne, baring that probably Renly. (Raegar was apparently competent, whereas Renly is a puppet, Robert and Stanis are unpredictable and too honorable, respectively.

Vimes has the same patriotism problem, combined with the possible loss of his family.
If he gets the support of a powerful noble like Tywin-Vetinari then he all of a sudden has more power than ever by about 20 fold. The city would quickly run out of cells. Ultimately though, I'm not sure anyone could protect Vimes from the nobles he would inevitably piss off.
Honestly in this situation Vimes would be more trouble than he is worth to Vetenari.

He might work as the watch captain of Winterfell or White Harbor, maybe Braavos.