It seems to me that progressive metal compromises melodic continuity for the sake or harmonic complexity and compositional elegance (ex: Vintersorg's "Visiosn From the Spiral Generator" album). Avantgarde metal can also have harmonic complexity and compositional elegance but of a different variety as it doesn't sacrifice melodic continuity as much (ex: Borknagar's "Epic" album). Avantgarde really pushes the artistic envelope in new emotional, thematic, and conceptual directions, and it's not uncommon for avantgarde metal to possess fusion influences (ex: Arcturus' "La Masquerade Infernale" album). But where fusion influences can push an original sound all the way into the category of avantgarde, I don't see how fusion would factor into the definition of a sound as progressive.
But I think that in contrast to metal in the genre of rock there is usually little distinction between progressive and avantgarde and in fact the term avantgarde typically isn't used, it's all called progressive... at least, this is something a rock person told me recently, I don't listen to rock myself.
Now technical metal it seems to me is sort of like symphonic metal in that there are a few bands that could be labeled purely symphonic but usually symphonic is a descriptive attribution like if you say a sound is symphonic blackened death metal or symphonic folk power metal. And obviously technical metal often happens to be progressive and vice-versa, but progressive metal doesn't necessarily have to be excessively difficult to play instrumentally speaking (ex: Ephel Duath's "Rephormula" album) and as well it can possess minimalistic influence.
Outstanding avantgarde bands that I haven't seen mentioned yet in this thread are:
Solefald
Age of Silence
Transcending Bizarre?
Peccatum
Diablo Swing Orchestra
Arcturus.
Plus I enjoy a couple songs from Korova, Cronian, and Chaostar.