With so many views, I'm going to put in my take. I've used both votes, first being a Major EA Victory (the war proper) and second being a stalemate (post war).
I'm calling the war itself as a major EA victory mostly because of attrition. The NR simply doesn't have the numbers needed to keep up with the EA. While most battles would start in the favor of the NR, being at range and firing long range cannon. I don't believe they could force the EA to stay at long range. Most battles will have the NR fighters out numbered three or even four to one. EA fighters given even a short amount of time would close on the NR capital ships and begin tearing into them. Another problem is that while EA ships may not have the same long range of the NR, they aren't lacking long range of their own. So a drawn out slugging match would favor the EA, every second in battle is another chance for a Starfury flight to volley into a NR ship.
It doesn't really matter who starts the fight and where, NR space seems small enough that its easy for them to respond quickly to threats and Sol is to heavily defended for the NR to crack by themselves. Result being a slugging war where the two just trade punches for a while. I don't think the NR would be caked to quickly. For the opening stages of the war, I expect the NR would give as good as it takes in return. However over time the NR's numbers would be worn down while the EA just continues to grow. Given a year, the EA would likely break the stalemate and drive the NR forces back to their home world for a final grand slam battle. No doubt epic, no doubt both sides fight with vigor worthy of the history books, but also no doubt as to the end. The NR forces surrounded and outnumbered in every way would just begin to break down.
Then we have the aftermath, post war which I voted a stalemate. Reason being that just as I don't see the NR being able to match the long game conflict with the EA, I don't see the EA being willing to mount the occupation needed to keep the NR on a leash. The EA could simply destroy all the shipyards and stations the NR built, but in fifty years the NR will have simply rebuilt them. But in the knowledge that fighting the EA simply isn't worth the wasted effort. As for the EA, I would expect the war to strengthen the EA's overall position in the galaxy. The NR were a constant worry for the LoNAW, and the CR was forever wondering when the NR would reach out for revenge. Coming out of a war like this, the EA will have absorbed the bulk of the NRs outer worlds and resources along with a vastly inflated warmachine.
Short and sweet, NR set back 50 years and the EA gets a 10 year jump in arms as the population slowly gears down from war level production.
Jinsei wa cho no yume, shi no tsubasa no bitodesu