@Dread
Now we can look at the number of Ships that have 3+, 4+ and 5+ Armour.

Also you do your argument a disfavour by ignoring shields, as with those the BTL damage drops off significantly while the "normal" weapon systems are less affected.
Also one of your statements is simply false, the Beijing Massdriver does not
almost double as good, on average
it´s damage against 4+ armour ships is 3 on average.
While the Cobra Laser does an average of 2,85. So around 5% more.
For 3+ armour those values change to 2,67 for the Massdriver from the Beijing and 2,71 for the Cobra BTL.
If you are referring to 50% of the cases you should rephrase your statement, lastly I think this is not really a fair comparison as the BTLs tend to spikes at both extremes. Furthermore this is mostly relevant in cases where ships are reduced to 1 or maybe 2 Hull, while on "fresh" or healthier targets the average damage is far more important.
I would argue that for those target types both weapons are quite similar with maybe a small advantage for the Beijing mass driver, if we also consider fire arcs, Flash and the high chance that the BTL does 0 damage.
Even for 5+ armour the difference is only 3,33 against 3 in favour of the mass driver so +11% as I mentioned earlier the bigger difference exists in regards to shields.
There the Cobra damage drops to 1,65 while the Beijing Massdriver only drops to 2 which yields a 17,5% increase.
Considering the Cobra Laser is a Cruiser sized weapon it is holding up rather well with the Battleship sized Mass driver Battery.
We could know be mean and compare the Beijing Massdriver with the Viper Laser which gives us:
5+ Armour: Viper 5,35 / 6 Dice Massdriver 3,33
4+ Armour: Viper 5,1 / 6 Dice Massdriver 3
3+ Armour: Viper 4,84 / 6 Dice Massdriver 2,67
4+ Passive: Viper 2,93 / 6 Dice Massdriver 2
While never twice as high as the Massdriver we see an increase in damage between 46,5% and 81,3%.