Starting with the main differences between both shields, i.e. the way they are working:
- The Passive Shield is always active and recharges by time, but adds fuel consumption per AU to the BattleSip (BS), while
- The Omega Shield shall/can be activated once needed, unfortunately it lasts just 5 minutes but does not cost additional fuel.
Of course like everything else in Hades, upgrading those shields enjoys more strength but rises the gas expenses. Apart from the high levels where the Omega Shield adds more health than the maximum Passive Shield, let's focus on the gas comparison at middle levels, e.g. starting with 8000 shield strength - Passive Shield level 4 vs. Omega Shield level 1.
How bad is the gas consumption?
To be able to compare them, let's take an intermediate Red Star mission, where the BS travels at least 4 sectors to clean-up some Cerberus. As the sectors in RS are 433 AU high and 500 wide, let's take the mean value of that, i.e. 466.5 AU. So the traveling would be about 1866 AU long (one way). With BS speed of 600 AU/min it will take 3.11 min just to move around. Include some fighting time and thus the total time may amount convenient to ca. 5 min, i.e. same as the activation duration of the Omega Shield.
Another simplification I make is to take just the comparable shield strengths, i.e. shield levels with same strength.
So, the Passive Shield lvl 4 (8000 strength) would need 287.4 gas to travel through those 4 sectors, where the Omega Shield lvl 1 (same 8000 strength) needs 600 gas to activate for just 5 min.
Passive Shield lvl 5 (9000 strength) needs 369.5 gas, where the Omega Shield lvl 2 (9000 strength) needs 800 gas.
Passive lvl 6 (10000 strength) needs 533.7 gas, and Omega lvl 3 (10000 strength) 1000 gas.
Passive lvl 7 (11500 strength) needs 698 gas, and Omega lvl 4 (11000 strength) 1250 gas - almost doubles.
Passive lvl 8 (13000 strength) needs 862 gas, and Omega lvl 6 (13000 strength) 1750 gas - already more than double.
Passive lvl 10 (16000 strength) needs 1231 gas, and Omega lvl 9 (16000) activation 3000 gas.
A reverse calculation from the Omega Shield gas consumption leads to the result, that Battleship with Passive Shield lvl 4 has to travel more than 8.4 sectors (6.5 min) to burn more than 600 gas,
Passive Shield lvl 5 has to travel more than 8.7 sectors (6.7 min) to compare to Omega Shield lvl 2,
Passive Shield lvl 6 more than 7.5 sectors (5.8 min),
Passive Shield lvl 8 more than 8.1 sectors (6.3 min), and
Passive Shield lvl 10 more than 9.7 sectors (7.6 min) to compare with Omega lvl 9.
Conclusion
If you don't move too much in RS- respectively WS-missions you don't need the Omega Shield.
If you are RS/WS-aggressor there is this nice trick to start the Omega Shield 1-2 minutes before entering RS/WS. Thus you have almost the double shield strength once arrived at the front line. This can't be compared to the Passive Shield.
