I like both, personally. But they’re completely different. It’s like comparing apples to oranges.
In terms of philosophical values, Star Trek is definitely more humanist and left-leaning in outlook; from its inception there was a strong pro-equality message (it was groundbreaking in the 1960s to have such a diversity of races and nationalities in the cast), and the ethical values of Starfleet and the Federation are definitely reminiscent of secular humanism. The crisis du jour is usually solved using reason and science, and the most intelligent and scientifically-literate characters (Spock, Data, Picard, Geordi, Jadzia, etc.) are the ones who most often end up saving the ship. Conversely, religion and spirituality don’t really seem to play a significant role; the only times religion is really encountered is on alien planets, where it’s usually in the process of causing some kind of bloody war or genocide.
By contrast, Star Wars is much more mystical and spiritual. After all, one of the central plot-themes of A New Hope is that Luke has to learn to rely on the Force, rather than on his own abilities. (Remember the scene on the Millennium Falcon where Obi-Wan tells Luke to put the helmet on with the blast shield covering his eyes, while he’s practising with the lightsaber? And Han Solo, initially a skeptic, eventually learns to believe in the Force.) The whole series is full of religious imagery and themes: faith, the battle between good and evil, being able to do anything if one believes strongly enough, and so on. This doesn’t mean I don’t like it – I do – but I’d see it as more pure fantasy, and I wouldn’t say it teaches good ethics in the way that Star Trek does.
I’d disagree with Shatner on a few points. I disagree that Star Wars is derivative of Star Trek; they’re only superficially in the same genre, and are really very different in their concept and premise. (I’d also say that ST:TNG, Voyager, DS9 and Enterprise were all worlds better than “classic” Star Trek; they were much more sophisticated in terms of plot and character development.)