Killing PDS requires combined arms. Instead of just bombers and invasion ships, you want to have at least some battleships for support. Destroyers and cruisers can also help to defend your invasion fleet.
First thing, and this is obvious so I'm assuming you did it, you have to knock the city defense to 0%. Enough airpower and missiles can take care of that. Use fighters to eliminate any fighter defenders.
Second thing, hammer the defending stack as your invasion fleet moves into place. It shouldn't take more than a handful of turns from border to attack, otherwise, the enemy will build more defenders and perhaps move in squadrons, as well as send more units into the areas.
Third thing, make sure you have enough units. You want at least double the number of defenders. So if they have 6 PDS, you want at least 12 attack ships. You can use battleships and cruisers to attack, but invasion ships are cheaper.
Fourth, if you've wounded the PDS down to about 2/3 strength, you are in good shape for victory. Less than that, you might need to hit them a few more turns, if you can afford the time.
Fifth, accept 50% losses if you take a star system. First thing, you want to use the least valuable invasion ships for the first waves. They're going to die, so why waste experienced units? Expect the first wave to use up one attack ship per PDS.
Invasion ships can take collateral damage promotions, which is one way to improve the value of these suicide attacks.
Sixth, when you're going for the kill, and have one good attack unit per surviving, wounded PDS, use the best attackers. Battleships often have better odds of victory than comparable era invasion ships. The idea is to win the fight, and you can't do that without risking some loss of valuable units.
In a recent game, I had an invasion force with 8 delta invasion ships and 5 battleships, plus a couple destroyers, up against a city with 4 omega PDS and a couple destroyers. The enemy had some battleships in the area, but not in the system itself. I had one carrier and one starbase in good support range, and a star system close enough that my delta bombers could reach it.
Even with good bombardment by about 10 bombers, the PDS were still fairly tough -- about 6 defense for the best. I dropped my newly built, low experience invasion ships on them, damaged them some more, then used battleships to pop the top two survivors, losing one. The invasion ships killed the rest.
It was rough -- I lost over half my force. But the system was taken.
So, no, I don't think PDS are too good. They are very good at what they do, but that's the point. It isn't supposed to be easy to take out well defended star systems.
Strategically, the AI (and for that matter, humans) can't easily afford to put massive stacks of PDS in every star system. Scout out your opponents, figure out which systems are relatively weak, assemble an attack force sufficient to take one of those, and go in fast. Don't give them time to build lots more defenders before you can take it out.
If the enemy is much higher in tech, winning can be extremely difficult. If you are matched in generation, invasion ships do fairly well against PDS at about a 2 to 3 to one ratio in cost. The expected losses are less than that, so the net cost to take a system doesn't have to exceed twice that of its defenders, and may be quite a bit less.
Having an edge in tech helps. Delta battleships are decent even against omega PDS. Once you have them, with carrier support you can blow away just about anything with light losses.
wow: 
:suicide: !!!) is near me (though in the Mini-Map, in the other side of the Universe...) and AFAIK only now New Earth started building Alpha PDS; this TOTALLY unbalances the game! (i haven't raging barbs). Use the WB to find it!
In the meantime, I can take a look at that one.
