Phase missiles have a chance to bypass shields...when they do bypass shields, they also bypass shield mitigation...
Consider a ship that is already at max shield mitigation (60%)...a laser that does 10 DPS normally would in fact do only 4 DPS (because 60% of the damage would be negated by shield mitigation)...a technology that grants a 10% increase to laser damage would then make this laser do 4.4 DPS (or 11 x .4), which is naturally a 10% increase in damage...
Now consider a phase missile launcher (that does 10 DPS) firing at that same ship (which has 60% shield mitigation)...without any chance to negate shields, the PM will do 4 DPS (just like any other weapon that does 10 DPS)...if we were to research a tech granting a 10% damage bonus, then we'd be doing 4.4 DPS (again, just like any other weapon)...however, the first 3 tiers of PM techs do not increase the damage, but the chance to negate shields...
Lets say you research a tech that grants a 10% chance to negate shields...for 90% of the time, the phase missile launcher used above will do 4 DPS...but for the other 10% of the time, it will completely bypass shields and shield mitigation, allowing it to do the full 10 DPS...so, if you average the damage done by this PM launcher, you get 90% x 4 DPS + 10% x 10 DPS = 4.6 DPS...
So, a 10% chance to bypass shields is actually comparable to a 15% damage increase...
If one were to have a 20% chance to bypass shields, then the average DPS would be 80% x 4 DPS + 20% x 10 DPS = 5.2 DPS, which is comparable to a 30% weapon damage bonus...
So, in essence, an x% chance to bypass shields is 1.5x better than an x% damage bonus, at least against targets with 60% max shield mitigation...
Against a target with higher shield mitigation (let's pick a high level Advent capital ship that maxes at 80%), negating shields becomes even more powerful...for a normal weapon, 10 DPS results in 2 DPS against this Advent cap (because 80% of the damage is negated by shield mitigation), and a 10% damage bonus would result in 2.2 DPS...but a 10% chance to negate shields would result in 90% x 2 DPS + 10% x 10 DPS = 2.8 DPS...so against a target with 80% shield mitigation, an x% chance to bypass shields is 4x better than an x% damage bonus...
Most weapons in the game get a 20% or 30% damage bonus through technologies...once fully upgraded, PMs get a 20% damage bonus and a 30% chance to negate shields...
Against a target with 60% shield mitigation, a standard 10 DPS normally results in only 4 DPS (as stated above, 60% of the damage is negated by shield mitigation)...the typical 30% damage bonus (through technology) would make that 5.2 DPS...but for PMs, all the tech upgrades would make for (1+20%) x (70% x 4 DPS + 30% x 10 DPS) = 6.96 DPS
So, PM upgrades amount to about 33.8% more damage (6.96/5.92 - 1) than most weapon upgrades...that being said, PMs are generally on the weaker side without any upgrades (for example, kanraks are easily outperformed by LRMs and illuminators without PM upgrades), so PMs are only problematic late game, capital ships, or against Advent...