Problems with Enterprise falling in the same timeline as ST:TOS or ST:TNG:
1/ Cloaking devices were unknown to Kirk and Spock yet at least 4 separate races in the time of Enterprise have cloaking devices and are encountered by the NX-01 including the Romulans. It is unlikely that Stiles with his Romulan obsession would not know about the First Contact and the existance of both cloaked mines and cloaked ships. Stiles would definitely have brought it up when Spock indicated that no one had made a practical invisibility device for ships.
2/ The war would have had to be fought between the last 2 episodes of Enterprise and was supposed to be a direct cause (as I recall) of the founding of the Federation yet is not mentioned by Archer, other Enterprise crew or Riker and Deanna.
3/ The war was fought with "primitive nuclear weapons" yet the NX-01 before entering the Expanse was equipped with phase cannons and photonic torpedoes (antimatter warheads).
4/ Impulse driven Romulan ships versus Warp 5 Earth ships? Warp 7 ships coming on line just after the wars end? Why would Kirks Romulans think that their slow ships stand a chance versus the Federation when their speed still lags the Earths ships from the war? By Kirks time the Romulans have not apparently even caught up to the tech the Earth had 100 years earlier and STILL they want a war? They are not that stupid. This only makes sense if in Enterprise Earth technology is accelerated (hints Cochrane got from the Phoenix repairs perhaps).
5/ The NX-01 encounters the Borg yet Starfleet of ST:TNG never seems to figure it out. Not even with experts like Data sifting through history for any information on earlier Borg victories (Guinan's people) and more importantly defeats.
6/ The difference in the two Rikers (Enterprise finale (fat) vs ST:TNG Pegasus). Rikers decision in the Enterprise finale is after a holodeck experience but in Pegasus it was when he found out that the cloak was intact. If it was only "fat Riker" suspension of disbelief would be acceptable (but a stupid choice by the film makers) but combine with everything else and the facts add up to a different history.
7/ The NX-01 is recalled to be present for the signing of the Charter of Alliance in the same year the Articles of Federation were due to be signed. Deanna says "You wish we could tell them all this Alliance will give birth to the Federation". A Federation that is supposed to form that very year. Not likely that both would happen so quickly. An argument could be made that the Enterprise had 2 consecutive full 5 year mission in which case the articles were signed in September and that leaves too little time to negoiate the Articles of Federation for the same year (and Deannas comments make it clear that this alliance is NOT the Federation) so the Federation is not founded in the correct year.
8/ The Federations (not Earths) first contact with the Klingons is disastrous and leads to decades of war yet in Enterprise the Archer does well by the Empire by saving one of their couriers and delivering information that keeps the Empire out of civil war. Where is the disaster in that? You could argue that his later escape (not a first contact) from prison and destroying Duras's ship might have provoked war but then it would have started years afterwards as it had not apparently occurred yet by the end of the series (8 years later after the destruction of Duras's ship).
Klingon relations (from a history onboard the Defiant in the mirror universe) don't get hostile until 2223 and continue for 70 years. This is ~70 years after first contact between Earth and Klingons in Enterprise and conflicts with Picards statement. (That history has other issues as well.)
So to sumarize first contact with Earth pre Federation did not result in war when Picard stated it was with the Federation and resulted in decades of war.
9/ Daniels states: "The events that are taking place are the result of temporal incursions. They're not supposed to be happening." Yet he ends up satisfied that the timeline is back on track even with the changes. That only makes sense if the voyage to the 1940s erased the expanse and the whole attack on Earth.
10/ The events of First Contact are apparently not recorded in the ST:TNG time but are in Enterprise. Archer knows of Cochranes talks about travellers from the future fighting cybernetic aliens but laForge (a big fan of Cochrane) does not. It would have been too late to classify Cochranes talks decades later laForge or Data would have known or discovered it.
11/ Picard does not have a model of the NX-01 an Enterprise that saved Earth and helped form the Federation, unlikely.
Assume that all of those cloaks had flaws and were eventually abandoned. Also Stiles was an expert on wartime romulans.
The war's role in the founding of the federation is implied by the Babel arc where Archer is able to bring together an ad hoc alliance of humans, vulcans, andorians, and tellerites
Most Earth ships don't carry photonic torpedoes, they still use spatial torpedoes. Also, photonic torpedo technology may have gone onto the back burner for a number of reasons. More powerful nuclear derived torps may have been developed, During the war production of the photnics might not have been able to keep up, forcing earth to fall back on its existing stockpile of spatial torps. Also, the fact that the photonic torps actually have warning labels on them with specific handling instructions indicates that they are more dangerous to deal with than the older spatial torps. Its conceivable that although Starfleet was willing to risk those dangers when an elite, experienced officer like Reed was the one handling the torps, but was less willing to risk using them in a hastily assembled wartime fleet.
The Romulans in Kirks time changed focused their design priorities towards making the cloak more practical, and developing the plasma torpedo. Remember despite the Romulan's lack of speed, it wasn't exactly easy for Kirk to bring down the bird of prey.
The Voyage to the 1930s dealt with a different opponent so it did not erase the expanse.
People might have considered Cochrane's words about the borg to be drunk talk, and revisionist historians would have purged it from the record because it portrayed him in an unfavorable light.
Relations with the Klingons in Archer's time weren't hostile, but they weren't friendly either. The way in which first contact occurred could very well have prevented a friendly dialogue from forming.
Picard had models of all "federation starships" named Enterprise in his ready room. Making the series pre-federation was meant to skirt the fact that Kirk's Enterprise was the first federation starship to bear the name.
Also, the moment of the federation's birth can be one of those hazy historical debates. Was it the signing of the alliance, or was it the signing of the Federation Charter at a later date.