Escaflowne was done with hand-painted cels, both
TV and movie.  I've seen enough Escaflowne cels to
know that it wasn't digital ink and paint :)

The stealth cloak effects were done with computer,
and the screen that Folken uses to communicate
with Dornkirk probably was as well from the look
of it.  The movie used computer animation in
parts, like the formation of Escaflowne's cape and
the sky scene at the beginning with the sun effect
on the "camera" and the 3d-ish depth effect with
the clouds.  Computer animation techniques were
used in places, but not all that much, and it
definiely wasn't overdone like a few other series
I could mention...

-- 
Matt Martin
http://nekomusume.net