3rd Edition gave us fighters that purported to have lots of flexibility, but ultimately failed at doing what they were supposed to be doing; you had no way of effectively stopping monsters from attacking the more dangerous characters, rangers could do the two-weapon schtick better (and easier), and numerous spellcasting classes could just buff themselves beyond anything a fighter could dream of, in- and outside of combat.
Really unless you wanted to ineffectually “button-mash” attack over and over, your only non-optimized option was to go with archery (though I hear spell-buffed rangers still got the monopoly, there).
4th Edition reined in spellcasters and gave fighters complex and meaningful options, allowing them to dominate the arena of weaponry (and tanking). No longer could clerics and wizards slap on a bunch of buffing spells--while still being able to bypass the hit point mechanic entirely and do other things--and no longer could druids wildshape into exotic animals that allowed them to make multiple attacks at their full bonus, before the fighter could even make a second attack at a huge penalty.
Players were rightfully concerned that the fighter was being dragged back into a darker age, where all they could do was fumble about and hit things for a brief period of time in which they could do it reasonably better than some other classes (or, more accurately, longer in an “adventuring day”). Classes that had skills, interesting features, and/or spells that let them affect groups of monsters, make skill checks that they normally could not (often with a bonus when it was not outright success), fly, boost their stats, and more.
Given that we were only shown a low-level snapshot, I cannot say for certain if the Next fighter was going to be like that. With the flat math, better skill distribution and flexibility, and heavier reliance on ability scores it is possible that a fighter might have fared better. They even got multiple attacks at level 2, albeit only twice per day, but at least it was without a penalty and could be used for more things than just attacks. However, wizards were still reliant on pseudo-Vancian magic, and fighters did not have any attack options except “hit it” (though to be fair, it was a crapload of damage).
For those concerned about going back to boring fighters, I think that this is promising news; fighters get dice that they can spend to add extra damage, reduce damage that they are taking, block attacks, and presumably much, much more. They refresh each round, which kind of reminds me of the warblade from Book of Nine Swords, though they had to spend an attack action to refresh their maneuvers, so it was more like every other round.
Most people are making comparisons to Dungeon Crawl Classic’s Mighty Deed of Arms, which basically lets you make a kind of special attack based on your description and the GM’s permission whenever your attack die--a die that you roll in place of a flat attack bonus value--comes up 3 or higher. Example deeds including things like gouging out a basilisks’ eye, impaling two monsters on one spear, and disarms. I would also comapare it to Stunts in Dragon Age, which you could use if the Dragon Die came up a certain number or higher.
I like it because it avoids going with a static bonus and provides the fighter with a simple resource to manage, both of which makes them more interesting. While I do not think that each class needs a unique resource management system, I think this is fine because it operates in a similar manner to 4th Edition in that it grants a sense of “narrative control” (and, ironically, the rate at which you gain maneuvers is similar to 4th Edition). I also like it because for those who want a simple fighter, you can just opt to use them for a damage bonus and call it good.