Crom and His Devils said:
Well, if you're going to do this amount of number crunching, go all the way. Draw up a half-orc straight barbarian or fighter of the same level as the dragon disciple, along with the same access to magic items, and then compare numbers. Look at the end-result attack bonuses, number of feats, class abilities, hps, the whole nine yards.
Str bonus to hit and damage by themselves really don't mean all that much in the grand scheme of things.
Well barb would have I think 18 more hp, rage for +6 str, rage enough time a day where it isn't an issue anymore, same number of feats, same AB of DD without enlarge +8str, 4 less attack bonus than the one with the extra str, uncanny dodge, dmg reduction of 3-. When he raged he would have +78 more hps,+3 more AB, still do 1-2 points less damage on a hit, have +2 to his will saves, and -2 to his AC. The DD gains darkvision, low light visions, immune to sleep, immune to paralysis, immune to one element type, +4 natural armor, natural attacks, breath weapon once a day, and flight at ground movement rate at ave manuverability, large size so a natural reach, oh and +2 int, and +2 chr.
If the DD went with fighter classes he'd have more feats, but fewer fewer hps equal to the levels of fighter, if barb, he'd gain rage+4 str-+4con,about 3 times a day,and uncanny dodge, a mix of fighter barb would gain mixed benefits. As is its seems balanced to me, maybe a slightly worse fighter than a straight barb, but more special abilities.
The primary benefit of the straight fighter types v the DD would be quicker BAB progression so they would gain extra attacks sooner. That would be slightly balanced by the DD gaining large size, and the only a great fool not taking a decent dex+combat reflexes. But end of the day same AB, same number of attacks, roughly same hp, does a little more damage per hit, a few more special abilities. The straight fighter or barb will be a little better at 6-9th level in other words about the same at 10-14th, and then the DD will look a little better after that.