That high elf tactica seems to have a lot of wish listing involved. Here's shooting some holes in some of his ideas.
1) Warmachine hunting has a turn 2 charge, and then the eagle running down the line. Without a vanguard, that turn 2 charge is going to be angled off the table, not down the line. That's why the Chief is better here. The 12" pregame move lets the 20" fly actually line up a proper over-run.
2) Wizard Assassination. Great Eagle does .88 wounds on a T3 opponent (which isn't a wizard lord). The elf poster seems to think that doing .88 wounds over two rounds, on a T3 wizard lord somehow equals 3 wounds, and that nobody takes ward saves on wizard lords. What's odd about this one, is that if the high elf player took 2 great eagles in 1 unit, and placed the 2nd behind the first, he'd get 2 supporting attacks would be able to try the assassinate in a single turn, instead of two turns. Chief is better here as well, as the S4 and S5 attacks (6 total) are far more likely to take out a wizard lord. Half with killing blow is a serious threat.
3) The rundown can be done by any unit. Charging a broken unit isn't exactly a tactical break through, and this can be covered by anything fast, or anything in the backfield (chameleon skinks).
4) Speed Bumps: the example is right out of 7th edition. 8th edition, the eagle is killed, forces a panic check on the 2nd eagle, and the opponent takes his free reform. You have slowed the opponent, but you better be packing enough shooting to make those 50 point speed bumps pay off. You also have to hope that your opponent can't deal with clearing the T4 no save model.
7) Combat res generator: Flank charge/rear charge into an existing fight is a good way to add +2 or +3 to combat res. BUT, the eagle has to be alive at the end of the fight, or you have only given up combat res. T4 no save isn't all that hard to kill for a lot of units, even those that are fighting to the flank or rear.
A 2+ save chief does this much, much better, and will wrack up quite a bit more combat res in the process (1 extra S4 attack, 3 extra S5 attacks, and the S4 is killing blow).
8) Avoid Stand and Shoot. If you're facing a big unit to your front, you should only stand and shoot if you think you might panic the big unit after killing the eagle (say, you have doom and darkness on the big block). Lone eagles do not get hard cover for being behind another unit. They have to be physically 50% obscured, just like every other unit of 1 in the game, like dragons, hydras, and chariots. Again, a 2+ save skink chief will survive a stand and shoot much better than an eagle. If said eagle was charging into my skink horde, I might stand and shoot at it. Hitting on 6's with 20 shots and poison should kill the eagle and force a panic check on the friendly infantry. If the infantry pass the panic, I can always then choose to flee from the infantry charge
9) Redirecting example is funny. It counts on, as the poster said, "Lets say due to either inexperience or Frenzy he overruns". If you're counting on inexperience or poorly supported frenzied death stars, you'll be winning anyway.
With all that said, some of the ideas are pretty good.
The long charge protection is nice. If one of your infantry blocks does make a long charge, having a flyer to block the enemy on the flank is very useful.
For anything that is a stalling action, the Chief is going to be stupidly better at it (again, 2+ armor at 89 points).
For anything that involves the flyer making attacks, the Chief is going to be much better at it (twice as many attacks, high strength).
For anything that involves sacrificing the unit entirely, the Great Eagle is better, as he's cheaper.
If 9th edition has ally rules (like 40K), I'd take lizardmen flyers over the great eagles. Both are good, but packing an armor save and having double the fighting power is totally worth the 56% cost increase.
-Matt