Well they both have mahogany wood, same fret numbers and styles, Grover tuners, rosewood fingerboards, a quilted maple top (if you get the black cherry finish for the Hellraiser), etc. The main differences I'm seeing is the Damien has a bolt on maple neck, and the Hellraiser has a three piece set neck. Personally, I prefer the set necks a lot but to each his own. There is also a difference in pickups, but I don't know much about EMG since I use passive pickups, so I can't tell you which is "better" between the two guitars pickup-wise. The Hellraiser also has binding. The Hellraiser also has coil tapping. I think overall the Hellraiser is a more versatile/higher grade guitar (just from reading about it), but to each his own. Best way to tell is play them in person =)

This is also just from a quick glance at them so there could be more differences.
Big difference - the neck heel. The Hellraiser's set neck is very carved down and quite easy to access the upper frets. The Damien has a Fender-like neck heel (which is MASSIVE). The Damien is a bit brighter due to the bolt on maple neck compared to the hellraiser's mahogany set neck.
Current Gear:
LTD MH-400 with Gotoh GE1996T (EMG 85/60)
PRS SE Custom 24 (Suhr SSH+/SSV)
Ibanez RG3120 Prestige (Dimarzio Titans)
Squier Vintage Modified 70s Jazz V
Audient iD22 interface
Peavey Revalver 4, UAD Friedman BE100/DS40
Adam S3A monitors
Quote by Anonden
You CAN play anything with anything....but some guitars sound right for some things, and not for others. Single coils sound retarded for metal, though those who are apeshit about harpsichord probably beg to differ.
Well if the Damien Elite is anything like the Damien 6 neck wise, the neck heel isn't that big, but i still prefer the heel on the Hellraiser series. 81 TW just means it can be coil tapped. I prefer maple necks myself, so that's mainly preference. Look used and you can prolly find a Hellraiser for the same price as the Elite. I found an almost mint C-7 Hellraiser with a hard case for like $450. So be aware if you buy the hellraiser new and try to resell later you're gonna take a pretty big hit. Having said that, they're both great guitars.