My $0.02:
Let's start from the Iceni- 3 BGreens, 22 other turrets 90k HP and 998 meters long, no fighterbay.
Make it 2x the size- 6 BGreens, 40 other turrets 180k HP and 2 km long, no fighterbay.
3.5 times bigger- 10 BGreens (imagine them overloaded for 3 minutes

), 50 other turrets, small fighterbay instead of the dozen more turrets that would fit on it, about 400k HP (at the cost of speed), 3.5 clicks long. Properly used, the BB could kill a Big 'C' (7 TerSlash, 6 BGreen, 50 other turrets, 1M HP), even though it has less than 1/2 the HP, and the C's fighters would have a hard time counter-attacking because the amount of turrets the Collie has would be defending a 2x smaller target.
Add the Carrier, being and overgrown Hecate, with 200k HP, similar anti-capship weapons, and a dozen more antifigher turrets. And, most importantly: >2x the hangars (thus more than a Big 'C', so it might defeat one without heavy ship support from any distance >8 km, given enough ammo and spare parts to keep the strike craft running)
Therefore:
2 ships that would take a lot less resources and time to build could take down a Big 'C'. However, a really expensive Big C Mk 2 could be strong enough to require both ships attacking at once to win.
Also- before anyone writes that these ships are too weak to survive- the first measure would be giving them strong sensors and a bunch of stealth fighters to see the enemy first and strike first; if that fails- these ships would need a quickly recharging subspace drive to warp out of trouble.
And finally- If one of these ships gets pwned and forced to make an evac jump, the other, knowing the enemy's position can simply warp in at a good position to counter-attack immediately, something impossilbe for a single jug.