The paladin Brilliant makes me doubt if you are being sarcasic. I case you aren't, both your examples (Brilliant and Eagle) would be much better if you used other slot types for anti-armor (large energy and medium ballistic, respectively) and medium energies for other roles (pd and long-range supression, in these cases). Even if you insist on wasting good slots on meme weapons, I'm still not convinced phase lances are worth using. Your HMG Eagle would be better off just using one heavy blaster instead of two lances.
It wasn't a joke, I also like phase lances a lot.
They are extremely good for phase ships and still nice for everything else IMO.
What he says.
The Heavy blaster is a better weapon overall, but it also consumes more flux per second than two Phase Lances combined AFAIK, not to mention Phase Lances work amazingly well when installed on hardpoints, while a projectile based weapon like the Heavy Blaster might give whatever has it installed an existential crysis.
The Paladin PD system stopped being a joke after it got buffed in 0.95.
It's the best per-OP point defence weapon in the game (not to mention belonging to the Energy category of weapons, which has notoriously bad PD options to boot), does 200 soft flux energy damage per shot at incredible efficiency and even has a weapon AI that saves 10 charges no matter if enemy ships are in range just to shoot at missiles/fighters.
It's a great weapon really, especially on the Brilliant since having no incoming missiles (and detonating Sabots at a longer range than they activate) really helps the Fearless AI when it comes to actually being aggressive. Here's another example of a Brilliant massively benefitting from a Paladin PD:
I eventually swapped some things out but the Paladin on the Overdriven Brilliant remained, a weapon making sure even the Fearless AI won't back off from enemy fighters or missiles
because there will be no such thing near it with a Paladin is quite the boon!