Substandard Bluth film is not a threat to Disney. Despite its beautiful animation, "Anastasia" falls flat on its face due to an extremely bad script. To date, the only good movies Don Bluth has ever put out are "The Secret Of Nimh" and "An American Tail" (only the original, not the godawful sequel). There is practically no character development and the final conflict between Rasputin and Anastasia makes absolutely no sense.
I especially found the music to be horrendous, especially the tune that plays during the scene in Rasputin's lair with all the bugs and worms singing (I cringed in terror every second during this scene). The only good song was probably the one Anastasia sings herself.
If Don Bluth is going to continue churning out such inferior material, then Disney really has nothing to fear. If you really want to watch an enjoyable non-Disney animated flick with good music and story, try "The Prince Of Egypt" from Dreamworks!