Total Rubbish i'm afraid, true the style of music is similar. But to sue there has to be a certain amount of notation that is exactly the same and there just isn't.
I have always thought the themes somewhat similar, more in feel than anything, but not "lawsuit worthy" as far as similarities go. You could also make a case it is a bit similar to the ABBA track 'Gimme, Gimme, Gimme' but again it is all due to the style of music. I can't think of any note in the theme being the same. And no note is from the theme of 'The Good, The Bad and The Ugly' (which is one of my favourites) though the music is inspired by Ennio Morricone's music so it has a pastiche quality in places.
I actually think it is a rather good theme in its own way.
Hadn't seen Hawk since I was a kid and watched it the other day. Couldn't get War of the Worlds out of my mind, it sounds too similar to be a coincidence to me.