I havenot read all the posts in this thread, so sorry if some of the points I make have been mentioned/debunked earlier. -It may be alittle long, but as with all verse vs verse threads their are so many possibilites that it requires a in depth response.
Only the top 20 Shinobi are really usefull, the rest would be used as edo tensei sacrifices. If good/bad guys work togethor on both sides-(So whole world vs madara, Obito, naruto and co.) then I can see the Narutoverse winning. If someone like me can come up with a feasible strategy, then I assure you ( given their feats) people like Shikamaru Nara would come up with it.
Before I start I am going to assume some things- The fight is on a planet earth, only basic knowledge is provided for eithor side, and as soon as the Narutoverse comes into being on our planet both sides know that a war is starting between both sides. -Victory for the narutoverse characters is if they can callopse/devastate all the worlds major powers, victory for the modern military is if they survive with a intact infrastructure and without sever casulties.
I am going to be using characters recent in the manga but at their "prime use" for example I am not including half dead naruto and sasuke- I will be using BSM Naruto and EMS Sasuke. Obito is going to be pre-juubi jink and Madara is going to be Edo Tensei + I am using Stage 2 Juubi. The reasoning is that the current narutoverse is fairly weak compared to a few weaks ago ( Sage madara has only a few feats)
Knowledge is power, and since I am assuming both sides have basic knowedge lets see how they obtain it. For the Narutoverse its fairly easy- have obito kamui warp to a outskirt city then have a yamanaka mind read. If it is decide dthe things like genjustu should not affect regular humans, than zetsu would be capable of obtaining information of the world.
, lets talk about Kabuto+Orochimaru: Lets assume kabuto broke out of Izanagi. Edo tensei has incredible war potential, especially since most modern weapons aer useless against them. from the saftey of the kamui dimension all the preparations can be made to utilize edo tensei ( obito can warp around random cities kidnapping people)- The edo kage's+ obito for mobility would be practically invincible. Kamui warp, hashirama and madara into a city- what is the current U.S. capable of doing to them? Mokuton forest, meteor, could probably destroy the entirty of NY city. So Day 1 the world learns about the streanght of NV. Seriosuly, what modern weapons takes out ET? Guns, tanks, nukes, would they do anything to ET? The U.S. had trouble finding 1 man hiding in the mountains, do you really think the world would be able to find a teleporting supervillain? PS madara can probably take out a city in less than a few hours- Deidera could continually use his suicide bomb justu to destroy atleast 10 kiometer squared.
So between kabuto , orochimaru, and obito the world is going to have trouble.- Remember, even if somehow they find Orochimau/kabuto, the justu willnot be released unless they purposlly release ET. So the only way to beat ET, to to physically restrain. Now, a nuke may be able to disintigrate a ET to the point of no regen, but its unlikely since Madara/Hashirama regened after the Juubi Bijudama ( easily above a nuke)- so if even a nuke may not take them out, they only other option is to restrain them? Do you really believe anything we ahve could restrain madara/hashirama?
Now, let talk about Naruto. All Naruto has to do is fight with shadow clones. If teamed up with kamui obito, he could warp in summon shadow clones, and warp out way before any military sees them. Naruto would easily be able to take entire cities by himself with this safe method. Or how about this, warp in, 10 seconds later bijudama, then warp out.
The rest of the narutoverse, while usefull wouldnot really contribute as much, the key players would be the Edo's ( because they are immortal) and obito ( because of his kamui) and naruto because of his shadow clones-
This point, while subjective I belive trully indicates why we would struggle so much against the NV. Its about Speed. haku moved so fast, superhuman genin couldnot even see him move. With the sharingan sasuke barely saw movement. Then, sasuke could barely keep up with lee. Against gara, sasuke matched lee's ( ungated) speed. Now, remember haku moved faster than humans can keep up with, now sasuke is several times faster than that.- the next bump in speed is against Naruto- Naruto with the kyubi chakra moved so fast, that sasuke couldnot keep up ( so several teirs above human eyes can see) After his third tomoa that changed. fast foward to shippudenn, Sasuke was praised for incredible speed.( at this point, Sasuke is several times faster than the Sasuke that moved teirs above what a human can keep up with. Sasuke, after an upgrade to MS couldnot keep up with the raikage, he barely saw him move. At this point, characters in Naruto are moving way to fast to be realistically touched by anything a human could throw. RM Naruto was seen to be faster than the raikages fastest punch- and then he got even faster in the cloaked BM. Logically, Sage mode is even faster. the point I am making, is that after Obito warps a shinobi like killer B, kakashi, naruto, sasuke, raikage, into a city- they would move way to fast to be shot at, the only chance of being hit is with AOE, meaning a bomb or nuke. The problem, is that with the shadow clones strategy nuking would do more harm than good.
While these strategies really heavily on kamui, what if we don't include it? Lets include Juubi Jink Obito instead.- We still struggle because juubi bijudama is leagues above nukes. One Bijudama ( the size of the juubi's head destroyed atleast a circumerfernce of 13 mountains-really much more because it whent into the stratosphere- a circular spher instead of the elipsical sphere that was fired would do more damage) A juubidama the size of the juubi was calced to easily be 8 times stronger ( its 8 times bigger) Obito can fire four of those at a time. So, that adds up to about 13*8*4 -( you can look at the panels yourself- the juubi is rediculous)
you think we would stand a chance against someone who could easily (he didnot look tired at all and went on to use other chakra extensive justu throughout the battle) destroy a range of atleast of 416 mountains in say, less than a few minutes. Even without kamui land to be safe ( kakashi can go there too) the barrier ( the one obito made not four kage)- could easily protect the narutoverse from anything the world could do.
Conclusion
-Combine a lack of tools to deal with the top teir edo tensei, Obito + kamui, Naruto shadow clones -( who in the hypothetical RSM would move leagues above a humans perceptions) the juubi, and you get a verse that can quite easily collapse the modern world.
-would the world be destroyed- probably not, would all 8 billion humans die? not likley at all
-in a war would I say the narutoverse won under the circumstances above- yes.
the questions to ask- edo tensei vs poisen -( well hanzo was suscptable to his own poisen, but Hashirma is supposed ot be a medical justu master so would poisan gas to anythign ( if it could hit)- remeber hashirama outran a bijudama across a mountain range.-
My favorite strategy -( have naruto die, revive him via edo tensei) then let him continually pump out shadow clones from the saftey of kamui dimension. - it may take awile, but I don't see any method the world could come up with to counter. So, in my above theory obito, orochimaru, and nauto+ some sacrificial fodder- could theoretically have a good chance at winning a war.
Note: I know my above situations take individauls out of character, but I am assuming the narutoverse acts as a united front against our verse ( similar to verses matches both sides try everything to their knowledge to win.