A very interesting question, and I'd love to see your findings in the end.
In my opinion an important distinction is WHICH edition war? The 2e versus 3e saw a change in publishers but much of the game remained the same. The 3e to 4e changes remained with the same publisher but QUITE a few sacred cows were changed...and "sacred cows" may minimize how much these features mattered to people. For me, Vancian spellcasting was not a cow...it was prime rib, baby.
Similarly, if we're exclusively talking about the 3e to 4e edition war, I personally prefer 3e over 4e, but have no war against it. It makes me sad that third party publishers dried up along with most of the support for 3e...but I'm glad Pathfinder provides for the edition (more or less).
However, when 4e was released I had MANY gripes against WotC. (These included, but are not limited to: the dungeon and dragon magazines which were quite poor when originally released, and were not even monthly; the promises made and not kept - at least until forced- such as releasing 4e versions of 3e books like Elder Evils; their general interaction with customers; the GSL release including the late date and poor original GSL; and so on). I was frequently characterized as hating 4e without that being the case. Just a heads' up that this might be worth parsing out...the change of the direction of the company at the same time as the edition conflates some of the emotion and reasoning. For example, one thing I don't like about 4e that I loved about 3e is robust third party support. I HATE WotC adventures for BOTH editions. But for 4e there are few and far between 3pp adventures compared to 3e.... So, you might say that a drawback of 4e is that the adventures aren't as good. But that's only true from a situational/business standpoint, and not from the standpoint of the game itself. I love the Open Design adventures for 4e, for example.
That out of the way, in terms of edition wars, my overall stake is:
* I would like to promote an edition I prefer over one I do not with the hopes that elements of that edition are carried forward as the game continues to evolve.
* The degree of change. I personally don't think 4e and 3e play as if they are the same game. I think this was intentional on the part of the WotC developers. I think some prefer one, and some prefer the other, but I haven't yet met someone who thinks they're "essentially the same, but with a few tweaks". I'd argue that "essentially the same, but with a few tweaks" might be true for 2nd edition to 3rd edition. They've completely revamped the game, and, as such, have begun catering to a new set of people. If you change checkers so much that it becomes chess, different people will want to play.
*...Which leads to some of the more philosophic questions you want to ask. Is it the same game? (To some, yes...to others, no.) What defines "Dungeons and Dragons"? Is Pathfinder D&D? Castles and Crusades? What can be changed and what can't and how do we define it? Similar to Agammemmon's ship...how many old boards can you replace with new boards and still have the same ship...and what if you take the old boards and build a separate ship with THEM (similar to the games mentioned).
*These questions lead to "issues" when talking with other gamers. 4e has been out for quite some time, but (no joke, this really happened) yesterday I went to the carwash with D&D books in my car and the guy there noticed. "A fellow D&D player?" he asked. "Yes, 3rd edition, I answered." This is something new for me compared to the switch from 2nd to 3rd. I'd say "yep" without mentioning edition then. Again, the degree of change here has been so large that, at least to me, it feels like playing a different game. It is no longer sufficient for me to say I play D&D, or if I were invited to a random game, I'd want to know which edition to set my expectations (though I'd be no more likely to play one than the other, assuming I wanted to join the group).
*In my opinion, there could become an element of philosophic dishonesty if a game is changed to such a degree that it is no longer recognized. It's re-defining an identity, and in the case of D&D this may be an identity that is a subset of the gamer's own identity. I'm not necessarily claiming this is objectively true from the changes of 3e to 4e (it is for me subjectively). However, if D&D morphed in 5th edition to, say minis with microchips in them, and they fought each other with audio outputs (all the dice and rules are pre-established for you! No need for math or rolling!!!). It would not be the same game as in the late 70s. There comes a point (that is different for different people....and this itself leads to the edition wars...where 4e isn't D&D for me, it might very well be D&D to someone else) when a game is changed so much that it is no longer the same as when it started. For others this change may have been 2e to 3e.
*In the end, I conceptualize it as Agammemnon's ship. There is no clear answer as to what "is" or "isn't" the ship. For each person there are emotional and logical preconceptions and rules that define where such breaking points fall. This is especially true when the changes are "better" to some people or "worse" to others. I wonder if I liked 4e more than 3e if I might be more charitable in conceptualizing them as "The same game". Similarly, if I was less irritated at WotC, I wonder if my overall perspective on 4e would be different. It's my opinion that the edition wars are very individualized and personal for each individual, and that you'll rarely see people, even people on the same "side" of the wars agreeing, as, in the end, it all comes down to the personal relationship you have with the game.
EDIT: AH, it's been a while. Not Agammemnon's ship. Theseus's ship. D'OH!
http://en.wikipedia.org/wiki/Identity_and_change#The_Ship_of_Theseus
*If someone took the gearshift off my first car (an 86 Toyota Celica), put in in a Porsche, and told me it was my first car, I'd sure as heck want to drive it. If someone did the same thing with a rusty 72 Fiat....well, I wouldn't want to drive it. It'd be a lot easier getting me to call the Porshe "my first car" than the Fiat. BUT 4e isn't better than 3e...and it isn't worse. It's better to some and worse to others. For some it's don't call that fiat my trusty, beloved Celica! And for others it's "Dude, I'm driving a porshe...This totally brings back the fun memories of doing donughts in my school parking lot. Maybe I'll do one for old times sake."