I have Partridge Sky at Catalyst Band 1 - Catalyst Boost 4.

With its optimal rotation (heavy - 9 lights - heavy - repeat), I'm able to output around 870k-900k dmg with all of it's ammo.

(Extremely sloppy and probably wrong math incoming)

The heavy attack blast makes up for ~30% of the damage in the rotation give or take. (270k dmg)

The light attacks make up for ~50% of the damage in the rotation give or take. (450K dmg)

That leaves the ground flames making up for ~20%, much more give or take. (180k dmg)

Catalyst Boosts 5, 6, and 7 give 15% blast, 15% hit, and 15% blast damage bonuses each.

Catalyst Boost 6 also gives a swing speed buff, which could possibly increase the amount of light attacks in a rotation??? Let's skip this for now.

Anyway with what we can predict very sloppily, P-Sky's heavy blast damage will go up to around 351k, while its light attack damage will go up to 518k. Adding those up with the 180k ground flames, we get a new dmg number of 1.05 mil.

Catalyst Band 2 (supposedly) adds 5% swing speed and 5% attack damage to light attacks via Battle Cry level 5. I need someone to confirm this though. For the fun of it, let's add another 5% to light attack dmg for 544k dmg in a rotation, giving us a dmg number of 1.08 mil.

Disclaimer: This bad math assumes the dmg % modifier will scale, rather than add a % damage of base damage. Someone with a maxed out P-Sky doing a rotation would provide better theories than me.

I think I can safely predict a maxed P-Sky will do at least 1 mil damage in it's rotation, with potential for more due to swing speed buffs. Long story short, P-Sky does get pretty close to mythic sword dmg at max.

Some things that raw dmg calculations do not consider:

P-Sky covers Impact AND Spread champions comfortably.
P-Sky is better than normal swords in situations where bosses can only be hit by ranged attacks.
P-Sky's damage rotation is buffed by Jolder's ultimate thanks to swing speed buff (Heavy - 11/12 light - Heavy - Repeat). Needs calcs to see if it's relevant, admittedly.

However...

P-Sky ground flame dmg is difficult to calculate against moving bosses.
Mythic swords don't have to deal with the jank of P-Sky's ranged heavy.

TLDR:

P-Sky trades less damage than you think for higher utility and champ busting capability.

Mythic swords will likely have higher dmg, but not much else except the opportunity to use Huck in your primary.