A SM57 was used in the original recording, both mics should offer similar results from what I've read, best thing would be to try both and see which sounds best unmixed.
Vocal chain is pretty much the same on the low and high screams.
ReaEQ
Waves DeEsser (any decent deesser will do)
SSLEQ
Waves RVox
Waves CLA-76
Waves C4
Waves L1
ReaEQ
Soundtoys Decapitator
All the vocals are sent in the vocal bus where Waves C6 does a bit of processing too.
Basically, the first ReaEQ highpasses the vocals, cuts some weird sounding mids and removes a touch of low-mids, then the DeEsser totally blankets the highs. The SSLEQ is used to boost the highs (at about 8k, going too low will make them fight against guitars anyway) and color the vocal sound, so that they sound bright and clear with all the compression, almost floating over the mix. In Waves RVox I shoot to about 6dB of gain reduction, in CLA-76 10 to 20dB (attack and release are set so it sounds good), C4 filters out unnecessary stuff without removing it totally (like some lows and low-mids), L1 removes about maybe 5 to 10dB and makes the whole vocals sound really in your face. ReaEQ is used to remove annoying peaks and whatnot, then Decapitator adds nice saturation (I used the N function, probably a Neve emulation or something). The C6 in the bus is used to remove a bit of low-mids again and keep everything under control now that all the tracks are together.
The high screams chain is the same, but with a bit higher high pass and more compression on RVox so the screams sound really smooth. IIRC I EQ'd them a bit differently in SSLEQ but nothing drastic.
Learning to scream well takes a LONG time, but with practice you'll be able to do it for sure! BTW if you use a SM57 or SM58, make sure to use a pop filter and to have the singer sing pretty close to the mic. To me, the tracks sounded much better on a mic stand rather than handheld (like Gareth originally recorded), so that's you and the singer's call.