We don't really know anything about Pilgrim technology. Their ships are never named or described - all we have is the briefest history of the war, put together from the Confederation Handbook, Pilgrim Stars and the movie/movie novelization.
We know they had fighters, jump capable warships and sloship warships... but no real details beyond that. We also know how naval tactics in general worked in that era, and that they were more focused around battleships. Fighters are for anti-shipping, planetary bombing runs, interception, reconaissance and such.
Here's {most of} what we know about the war itself. Feel free to add anything I've missed so we can have a complete history:
In 2462 an armed Pilgrim sloship (Hopper drive vessel) arrived at the moon and engaged in some gunboat diplomacy - demanding a meeting with Earth's leaders. This ended with the Treaty of Luna, which gave the Pilgrim Alliance rights to all habitable worlds within 50 years Hopper-drive travel of Sol in exchange for a promise of non-interference and limited trade agreements. Thus Terran expansion was very slow until the invention of the Jump Drive in 2588, which allowed colonies to spring up overnight outside the fifty year travel sphere. A hard-line militant facton took control of the Alliance in 2615, prompted by Pilgrim fears over the Terran Confederation's rapid expansion (Earth-bound humans being divinely cursed per Pilgrim theology).
The Battle of Titan. On 2631.244 a Pilgrim fleet jumped to the Sol system to attack Port of Titan space station (near Saturn), the exit point for Terran Confederation jump-drive ships. Having expecting little resistance from comparative primitives, the Pilgrims were shocked by the strength and dedication of the human fleet. Three days of fighting ended with a retreat, the Pilgrim fleet having been unable to destroy the station.
Pilgrim sloships attack Dewey Station Five, near Pluto. A Confederation Bengal attempting to target a Pilgrim sloship accidentally hits the station's south wing, killing 1400 civilians. Pierre Christian and Marie Sousex Deveraux are among those killed; their daughter, Jeanette, is rescued. Terran Confederation Naval Command Authority classifies the incident.
Refusing to accept a new round of negotiations with the Confederation, the Alliance settled in to fight a guerilla war in the new Confederation colonies. On 2632.017 Alliance forces attacked and destroyed a Confederation military outpost and mining colony on Celeste. This prompted a formal declaration of war by the Confederation on 2632.018.
Arnold Blair is recalled to active duty at Titan. He serves onboard the carrier TCS Harrison. In twenty-five months he earns double ace status with eleven fighter kills and two capital ship kills. He is awarded two Blazes for Conspicious Gallantry before joiing the secret Grand Fleet design team in 2633. He serves as senior cyberneticist, earning a Conroy Medal and a Senatorial Commendation for designing maneuver control software.
Midshipman Tolwyn serves as an engineer with the Grand Fleet design team.
A young Captain James Taggart is assigned to Confederation Intelligence Services. He is paired with an operative named Ebeneezer and the two pose as Pilgrim free traders. He later remembers the experience for having attending prayer meetings, con/crit sessions and transcendence dances. He infiltrates Peron, where he becomes acquainted with Solomon Truepath and Devi Soulsong, the grandfather and mother of Christopher Blair.
The Confederation braced itself onto the defensive, concentrating its resources to build a massive fleet to respond to the Pilgrim threat. Buoyed by their initial victories, the Alliance campaigned against more distant Confederation colonies - capturing several worlds and forcing millions into slave labor. The Confederation military received harsh critisism for its refusal to liberate occupied worlds both at home and abroad, where the Alliance interpreted their lack of reaction as weakness.
Arnold Blair returns to the front lines, serving another tour aboard the TCS Foster. He scores three more kills and earns a citation for bravery.
The Confederation develops the Concordia class SuperCruiser.
Both of William Santyana's parents serve with the Pilgrim Alliance military.
A special effort is made to eliminate rare Pilgrims with hypersensory perception abilities. These powerful Pilgrims are allowed to attack and then eliminated after power usage has made them weak.
Sandra Gregarov serves as an especially succesful Line Captain.
The parents of Amity Aristee, Pilgrims, betray the Pilgrim Alliance. They are executed for treason and their former friend, Frotur Johan McDaniel, takes charge of educating their daughter.
Mikal Taggart, adopted father of James Taggart, is killed by Pilgrims.
2633.235 - the Terran Confederation's Grand Fleet is launched, culminating their war strategy of preparing for a single offensive campaign to end the conflict rather than allowing a drawn out battle over resources. The fleet includes the first Broadsword bombers ever built. In five months the Terran fleet captures Centauri, Sirius, Cygnus, Frase and then Bradshaw. The rapid advance ends at Peron, a Pilgrim planet in the Luyten system. Desparate after heavy losses the Alliance gambles everything on holding the agricultural world. A seven-month siege breaks out around the planet, with both sides striking back at eachother in increasingly bloody counter-attacks.
William Wilson serves as a battleship commander.
On an occupied world the father of Paul Gerald is dismembered until bleeding to death by Pilgrims. Gerald's mother discovers the body in their back yard.
On 2634.288 the Second Grand Fleet, 1.5 times the size of the first, arrived to reinforce the survivors of the first. The advantage to the Confederation is overwhelming and Peron falls two weeks later. On 2634.301.0900 Major Arnold Blair disobeys orders and heads to Peron in a stolen Merlin fighter to rescue his wife, Devi Soulsong. She dies in a Terran Confederation attack and he is killed when an automated stratospheric defense drone destroys his fighter. The nature of Blair's indiscretion is classified by Grand Fleet Information Office for reasons of morale. More Pilgrims die at Luyten than in any other engagement in the war, leading to the battle being later called the Peron Massacre. "Remember Peron!" remains the post-war Pilgrim cry for many years.
1st Lt. Tolwyn commands a battleship as part of the Second Grand Fleet.
The invasion fleets jump to Beacon on 2634.359 where they are met with an offer of unconditional surrender. After six weeks of negotiations the peace accords are signed at Cygnus, with the alliance agreeing to stand down its military and dissolve its government in exchange for safety guarantees for Pilgrim civilians and limited autonomy for several worlds. Final casualties number in the millions killed.