Where some extra hit points = 28 - or more than a third of your 81. My guy is tougher. And has DR. And Uncanny dodge.
Those are definitely nice things. Barbarians do have their advantages.
And let's have a look at the restriction raging imposes, shall we?
Off the top of my head the only three skills you can't use from that list while raging are Appraise +2, Diplomacy +4, and Knowledge (geography) +2
"Inability to use most skills." Right. Appraising, combat diplomacy (as opposed to combat intimidate), and knowledge (geography). Some restriction given you are fighting for your life.
You ommitted uses of untrained skills. Your Blackbeard has to stop raging simply to attempt a Bluff, to Search for something, to tie a rope around himself, or to attempt any Knowledge check whatsoever.
Toughness? Mine can almost take those 120hp damage - and has DR. Yours isn't close. Skills? Mine beats yours. Ranged combat? Mine beats yours. Melee? Apparently you think 33% of your hit points are worth 2 points of AC. Right.
It probably is. If my opponent needs a 17 or higher to hit me, it's literally true, without taking into account all the reasons you wouldn't want to be hit at all.
And an edge case iof combat more than eight rounds after the melee starts is worth a lot.
Pfft. Edge case? I've seen a barbarian's rage expire many times. And in fact, in my 1st to 20th level game, the only full BAB character who ever died was a Barbarian.
At what? He's better with skills. He's better with ranged combat. He's better in melee combat that doesn't go beyond 8 rounds. And he's a lot tougher.
He's not tougher at all if the melee combat runs more than 8 rounds. He's only marginally better in melee for those 8 rounds, and if he wants to do something other than attack during those 8 rounds, may find his choices limited. I don't see how's better at ranged combat, unless "the same to-hit, with a lower AC and inconsequentially higher hit points which will not be all that high when a ranged combat WILL run eight rounds or longer in most cases," is better.
And barbarians don't have to be. They can wait until the critical moment then hit as hard and brutally as possible to turn the tide.
And hopefully their opponents will adopt exactly the same tactics, despite not being barbarians, and not use defensive tactics, withdraw, or focus on ranged attacks.
Anyway, this serves no further purpose.
It does to me. Obviously, it isn't serving much of a purpose to you since each level of argument is explosing more weaknesses in your argument.
Your Barbarian is a slightly better shock trooper, but as a generalist, well, Fighter, he just doesn't stack up, and he won't. The only things really in his favor are a few skill points, DR, and Survival as a class skill. Rage is over-rated; this is not hard to conceive, and in actual play, is very easy to discern.
Because of the peculiarities of the skill system, your Barbarian does slightly better at certain skill checks, but being amazing at those skill checks is not Blackbeard's archtype, nor is your barbarian more competent at those skills to a great degree anyway. Implicitly, you seem to believe Barbarians are simply better at fighting; I am not sure why you believe that to be the case. Rage offers substantial bonuses, but it is a specialized and limited approach to combat.