This discussion is forcing me to make up my mind about these "genre" distinctions.
My first thought about "symphonic" as opposed to "heavy" comes from what I hear in movies and TV episodes.
I wouldn't think of using "symphonic" to describe any rock music unless a synthesizer player imitates an orchestra.
That could be "Gates of Delirium" by Yes on the Relayer album, but everyone said they were progressive rock.
So for me, hearing a heavy metal band providing a wash of sound without being a lead guitar solo could be symphonic.
Here in this heavily electronic Niagara Peninsula, there are many subtle differences for bands with loud, distorted sounds.
Grind-core, punk, steam-punk, emo, screamo, screamo-emo, thrash, heavy metal, factory, altered states, goth, wicka wicked,
hard rock, psychedelic rock, raunch, classic rock Black Sabbath style....
and I have to include DeadMau5 and Rezz, electronica DJ's who are pumping out the loudest and most famous sounds right now.
For me, the biggest difference between heavy guitar driven bands comes down to is a guitarist using a seven string guitar?
If that extra bass string is there the deep chords can become demonic sounding, an entirely new range of deeper sonic delivery.
I have to mention TINKICKER, one of my favorite bands from Denmark... uh... melodic metal? axe-swinging Vike-rock? Thor-bangers?