I'll talk about Escaflowne last, because there will be spoilers, and because in a way it's the odd man out of this week's picks. Nadesico and Dai-Guard have a common plot point - not the "humans battling aliens" plot, though there are definitely aliens in both, nor the "giant robot" plot device, though Dai-Guard is in fact a giant robot of the kind parodied in Nadesico's "Gekigangar 3" show-within-a-show, and in addition Nadesico has the Aestivalis mecha. No, the unifying plot point for these two anime is the "private military company going to war because the government is too inept/backwards/cheap (pick one) to use the only weapons effective against the aliens." In Nadesico, Nergal Heavy Industries builds the eponymous space battleship and deploys it against the Jovian Lizards, upon whom it wreaks great devastation; in Dai-Guard, 21st Century Security Corp. built their giant robot to fight the first invasion of the Heterodynes (no relation to the heroes from Girl Genius) but it lies inert as a budget sink and sometime tourist attraction before the Heterodynes return and an impulsive young salaryman takes it into action to save some innocent civilians. Both series are fun little romps, not to be taken too seriously, and both poke fun at the sometimes ossified bureaucracy that runs both the Japanese government and, occasionally, Japanese corporations. I think anyone that appreciates Keith Laumer's "Retief" stories will enjoy both of these series, which show bureaucrats at their dangerously inept worst.
And now to Escaflowne. Spoilers follow.
I liked this series, but as far as I'm concerned the ending sucked. Hitomi didn't get any of the guys she was faunching after, people who badly needed to die (Dilandau and Dornkerk, especially the latter) were still using up air at the end of the series, and there were some serious plot holes that I think could have been wrapped up had the series gone on a bit longer.
I also have a hard time believing that the destruction of Zaibach's Fate Alteration Device by Van and Hitomi was going to be enough all by its lonesome to stop the fratricidal war that ripped apart the Alliance once Zaibach's armies were destroyed by the superweapon, and that Dornkerk was stupid enough to believe that people left to their own devices would automatically choose peace and brotherhood over war and avarice. There is nothing, nothing in his behavior up to that point that made me think he was that starry-eyed about people. This is a man who was willing to sanction the death of an entire nation so that he could get his hands on Escaflowne and keep it from screwing up his plans. This is a man who allowed (or ordered) the hideous reshaping of Celena Schezar into the sociopathic killer Dilandau! And we're supposed to believe that he thinks people, given the power, will build Paradise? Sigh...
There is a message in Escaflowne, and it's telegraphed in the episode where Van and Folken return to the ruins of Fanelia, which has been overrun by land dragons now that all the knights that kept them under control are dead. Unfortunately, people are not dragons, and not all fighting is caused by fear and anger. Sometimes it's greed, and sometimes it's just evil. It's also worth noting that Hitomi's horror at the pleaure Allen and Van derive from fighting is pretty immature - they are fighting for the right, and why shouldn't they enjoy the thrill of testing themselves and their skills in the adrenaline rush of combat? It's said that a lot of surgeons enjoy the cutting and the blood involved with their work, but it doesn't make them evil, or less skilled at what they do.
All that having been said, this is still a good series. The art is good, the music is good, and if the story didn't turn out the way I would have liked it to, it's still pretty good and well worth seeing.