Ya an Empy weapons "magian trial" consist of fighting a series of NMs, then VNMs, and then obtaining items. For the first 2 parts you can group up and not have to compete for the mob, but after that with the items it does take more time.

For relic it's obtain currency, materials, an item from glacier and xarc, then to get it to 90 it's kill an obscene amount of mobs with using WS for finishing blow, then beat some boss NMs in the dyna areas and then kill the NM that was attached to your glacier quest requirement lol. Considering the two the above is a lot less hassle for a greater reward compared to what relics offer.

Then mythic is just a big mess of pre-reqs with it's own currency that require one to go across a broad range of events to obtain what they want, granted the only competition persay would be obtaining alexandrite since the rest can just be grouped to obtain I believe.

Using Great axe as an example it's
Name-DMG-Delay-Info
Brav--133-488---ACC +35, Eva down -30, Occasionally does 2x dmg "Ws offer Def down and decreases dmg taken"
Uko---131-482---STR +15 Aftermath: Occ does 2x dmg
Conq--129-504---Berserk IV (Let's say 45% if it goes up 5% each rank) Aftermath (Acc/Att/Occasionaly att twice)

In terms of difficulty I would say
Mythic>Relic>Empy
In terms of strength I would say
Empy>Relic>Mythic

This is all just opinion based on the info given but with the following I see
Bravura:
Pro:
Ability to replace ACC gear with strength
Occassionaly att twice always active
Def down on WS
DMG taken reduced with Relic WS use
Con:
Lack of any WS mod to help with dmg

Ukon:
Pro:
Strong Weaponskill
STR mod on weapon
Con:
Occ does 2x dmg only effective as aftermath (granted it could be challenged by the fact that aftermath will always be active once used since TPing is pretty fast to an extent so there may be a few second you are actually without the occ deal 2x dmg mod)

Conq:
Pro:
Berserk Mod
Con:
Weak aftermath
highest delay of the 3

Overall in order to fix relics and even Mythics to an extent SE needs to consider how to make them their own unique tool.

When SE made them I think they considered
Relic=Heavy Damage + enfeeble
Mythic=Job specialization
Empyrean=Heavy Damage

The problem lies with the overall utility given with relics, with the example of Great Axe to an extent while on paper it looks like a great tool with the use of /nin and shadows the act of reducing dmg taken isn't as good as it should be.

With Mythics the overall job utility isn't fairly balanced for each job leaving some jobs with weak specialization while other jobs get ones that are actually good for them.

Empyrean is basically the tool which a majority of players use as their main strat which is dealing the most amount of damage as possible and taking the foe down as quick as possible.

In terms of utility I think it should be
Empyrean: Heavy Damage
Mythic: Job specialization
Relic: Hybrid Heavy damage + Job specialization

In this instance Empyrean would have an equal damage dealing weapon towards Relic and Mythic would offer the most specialization but Relics would be able to balance themselves with Damage and specialization which overall if done right should outshine the two.
Name-DMG Max-Ability Max--Ability Max
Bravu-160------Berserk III--Defender III(reduce dmg taken 6%)
Ukon--160------None-------------------------------------------
Conq--140------Berserk VI--Defender VI(reduce dmg taken 10%)

Basically the idea is to try and draw a unique nature for each weaponry, if you just want straight up damage you go for Ukon, but if you want a weapon with heavy dmg and some job specialization you aim for Bravu, finally if you are more intersted in augmenting your job's abilities you aim for Mythic.

With this change in mind they should allow the Reilc/Mythic to be more customized based on the user's preference, by allowing unique mods be added to the weapon.

When you look at Mythics as a whole you'll notice that to an extent it's a big mess of what were they going for, some weapons have trait augment, others have 2hr augments with stats and then others are abilities and stat augments, or just ability augments lol.

NIN, WAR, SCH Mythics:
NIN=MACC, Enmity +, 2hr augment
WAR=Berserk Augment
SCH=Weather: ACC, MACC, Enmity -, MAB

Considering the above it seems pretty imbalanced. I would say that judging from the three SCH has a decent augment for itself it's only downside is needing weather active to make use of it. If I were to revitalize Mythic I would allow the user to create their personal augments on it, like the add-on rewards.
Let's say your base point value is 20 and with each magian upgrade it goes up 10 so by 90 you would have 50 points to work with.

Now for Conquerer I would say:
Att/Acc augment=5 points
Ability augment=10 points
Trait augment=5 points

So let's make Conquerer a
ATT +10, ACC +10
Bereserk augment
Double Attack augment

Then at 80 you gain 10 points to work with so you could do
ATT +20, ACC +10
Bereserk augment
Double Attack II augment

With this idea one thing to keep in mind is the level of a trait can't go above the rank of the weapon so at most by 90 the same stat can only be augmented up to IV.
85
ATT +30, ACC +10
Bereserk augment
Double Attack III augment
90
ATT +40, ACC +10
Bereserk augment
Double Attack IV augment

It's just a quick idea that would make mythic/relics a more enjoyable objective to obtain over the empyreans which focus purely on damage. I"m curious to how they plan on fixing it up to balance it out better but it would be cool if they gave the ability to properly augment your weapons to customize it to your play style rather then a mandatory setup for it.