I'm late to the thread, but here goes...
What's at stake for me:
A hobby that I enjoy, that is incidentally backed by several corporations.
In my opinion, the Edition War started because all of those involved really enjoy this hobby. Why else would we spend this much money, time, and energy on it? (Note that I am explicitly excluding trolls and people just looking for a good argument, but including those interested in reasoned debate.)
Each set of "official" or 3pp rules and supplements released has an impact on how we play the game. Will this make it more or less fun? Will this make it easier or harder to play? For many, will this change encourage or discourage new people from joining our group?
These new additions/clarifications, even up to new editions, have a sometimes conflicting set of questions from the companies that produce them: Will this sell well or poorly? Will this expand the number of gamers (increase the market) or reduce it? Will this be popular or unpopular? Is there enough of a market for this product to make it worth producing/distributing?
This is what's at stake for me. Each new edition - going all the way back to OD&D - has introduced elements that make it more fun, easier to play, and encouraged new people to join in. By the same token, they've also introduced things that are less fun, make it harder to play, and discourage new people from joining in. In general, the number of (and amount of fun generated by) the positive things has outweighed that of the negative things -- for me; until 4E.
4E mechanics are a significant change - so significant, that even the designers specified that existing 3/3.5E campaigns can't be ported over. If you want to use the new rules, leave everything that you've built before behind. You can't carry many of the fun things from previous editions into this current one. That's changing a lot of fun things about the game, suddenly, harshly, and economically.
As an example of the fallout from this, consider the above questions again (deliberately NOT trying to start an Edition War - consider these statements of my perspective and experience):
* Did that make it more fun or less fun? For many of the people I game with, that made it significantly less fun. For others, the opposite is true.
* Did that make it easier or harder to play? 4E streamlines many problems from 3/3.5... and introduces whole new timesink roadblocks. The purchasing plan to get errata and "core rules" updates also makes it harder, in my opinion. 4E definitely lightens the DM's workload, and that has an exponential effect on the ease or difficulty of play.
* Will this change encourage or discourage new people from joining our group? My experience (admittedly limited) is that it discouraged older gamers (and older new gamers) from joining in with any group. It seems to have encouraged some new, younger gamers. But not much in my neck of the woods.
Previous edition releases have done all these things and more, but nowhere near to this degree. 4E was designed to break with every previous edition. This is a first in the game's edition changes. (And subject to very informed counter-arguments by peers gathered here. But the OP asked what's at stake for me.)
The net effect of this is frustration for me, being painted with an overly broad, insulting brush repeatedly; and a much reduced participation with other gamers of any persuasion. Reasoned discussions about the merits of the rules, for any edition, are now a pointless exercise for me - even on ENWorld. This has had many far reaching and, I think, many unintended consequences.
I want to play with other gamers, new gamers, old gamers, and even my regular crowd. The introduction of 4E has made that needlessly ten times harder. I want to talk with other gamers about rules, interpretations, scenarios, DMing, and similar game-related matters... but the current rules create a barrier to common language and understanding.
New gamers have all sorts of cool ideas and interpretations! That's harder to get to, now, with all the vitriol and rules barriers. Older gamers have tried stuff out over a longer period of time, and have all sorts of neat experience! That's harder to get to, now, for the same reasons.
Basically, gamers are split more fundamentally and deeper than any time I've seen before - going back to pre-T$R days. That division will get wider, as long as economic decisions (from those companies' sometimes conflicting questions mentioned above) are pursued.
And to try and meet Umbran's double-dog dare:
My game is super-cool because the half-black dragon/dwarf monk ripped the head off a hill giant and used it to club an ogre into putty... ON ONE ATTACK!!!
My game is also super-cool because the human bard won the entire adventure by ensorceling the mountain giant barbarian leader, AND SUCCEEDED!!! It was really super-cool because the other players (and their characters) were cheering him on!
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That's my brief perspective on what's at stake for me. There is more, much more, but I'm too tired and it's too late at night... and I haven't had near enough beer for this.