The Eberron system is different from the Unearthed Arcana system. I'm currently running a game with each and prefer the UA system. Really, though, most people use them to modify d20 rolls and stabilize when dying, so there's little difference in actual play (both systems handle both those situations the same). I just feel the UA system has more potential for players who want to take advantage of it.
Action points definitely don't seem to unbalance anything. You only get a handful each level, so no one is consuming them like candy. They really provide two major features.
First, they provide an insulation against that one crappy roll. The player gets the chance to boost their failed save or to fiat stabilization at -8 hps. If the players are generally playing smart and get one bad roll, it's not likely to result in death, but they don't have enough APs to evade Darwin. Also, if I, as GM, slightly misjudge an encounter's strength, I don't have to fudge anything because the players have that net.
Second, it lets the PCs occasionally do something really cool. I've noticed this as the PCs get ready to level -- which, tends to occur at the climax of an adventure, nicely enough. Most PCs will have a couple left over and are itching to not "waste" them (use 'em or lose 'em), so they start doing a few tricks and pushing for unlikely successes. The most common (and, potentially, effective) use in this mode has been the "take an extra attack during a full-attack action", which has prevented that last, devasting round of attacks by the BBEG more times than I can remember.
The OGL/UA rules for AP can be found
here.