In theory. I'll admit that Crossbow headshots from a Level 4-5 Sharpshooter do some sick damage, but you're forgetting that the Support Specialists get their damage bonus with the Shotguns as well and that the Patriarch has at least some level of damage resistance on Sucidal...
My calculations
was with the x1.5 shotgun damage or x1.4 explosive damage that support specs get.
Patriarch get no damage reduction (unlike the Fleshpound that only take 50% of all non-explosive damage), but he get more HP.
Patriarch have 4000 base hp.
Beginner x0,5
Normal x1,0
Hard x1,35
Suicidal x1,75
More players add up HP as well. The Patriarch add 75% HP for each additional player besides the first one (other mobs add less, Scrake 50%, Fleshpound and Bloat 25%, Gorefast 15% and Siren 10% - rest does not scale with player count at all). So a six player patriarch have 4000 * 1* (1+5*0,75)=19000HP (which is consistant with the "1900..." you see at the cut scene).
A suicidal Patriarch in a six player game have 4000 * 1,75 * (1+5*0,75) = 33250HP (which is consistant with the "3325..." you see at the cut scene).
Xbow have a base damage of 300
Sharpshooter deal 50% more xbow damage
Xbow have a x6 head shot multi
Sharpshooter deal 50% more head shot damage
300 * 1,5 * 6 * 1,5 = 4050hp
Hunter shotgun pellets have a base damage of 50
Both barrels shoot 10 pellets
Support spec deal 50% more shotgun damage
50 * 10 * 1,5 = 750HP
LAW have a base damage of 650
Support spec deal 40% more explosive damage
650 * 1,4 = 910HP
Everyone say support spec is so overpowered, but i dont know....
What make support spec powerful is the 100% shotgun penetration that let them kill multiple standing mobs down a corridor with one fast single shotgun blast from the hip and their extra nade supply.
Sharpshooters have most single target damage per second in the game which let them take out a scrake in two shots without enrage or kill siren at long distance with one shot even if there are multiple mobs blocking the view.
Berserker have a hard time with crawlers but is probably the best perk when it comes to decapicate fleshpounder or save a swarmed team member. Faster movement and immunity to root let them get out of tricky situations. They often dash out most damage of all perks in any given round.
Commando with their 40 clip gun are excellent at killing crawlers and stalkers at close, mid or even long range due to the x2 scope they have. They can also track the Patriarch when he stealth to heal (interrupting his heal is alone worth several thousand damage).
Firebugs are pretty strong at everything. Short range, mid range and even long range. Both swarms of Low HP mobs or single strong high HP mobs. Setting Patriarch on fire help a ton when tracking him during his stealth pase. Flame grenades cover a huge area... Only drawback they have might be long reload time and shortage of ammo on maps where your party move around.
Field medics just never die. They are almost always the last man standing and they can outrun everything, even the Patriarch. Good perk to help out. Healing your party and helping out berserkers and support spec by taking out high priority low health targets (such as crawlers and sirens).
To be honest all perks have their advantages and disadvantages. It all comes out pretty even at the end. It mostly boil down to what type of gameplay you enjoy the most.
I love one-shot-kills, so I play a sharpshooter. Whats your game?