Star Trek vs Star Wars physical ship strength

[Elheru Aran]

Or the Cardies are significantly better on the ground than they are in space, and the Feds lack the will or the capacity to root them out.

Certainly possible (though, arguably, a kindergarten class would be better than the Federation on the ground...). I haven't watched enough DS9 to know whether or not the Cardies fought the Feds before the Dominion came onto the scene. It's possible that the Feds simply didn't deploy any serious fighting ships on the scene beforehand, and suffered some losses as a result, and chickened out.

[Lord Revan]

from the TNG and DS9 I've seen I got the impression that Galors were a serious but minor threat to Federation ships, basically a starfleet captain would have a Galor seriously but if did that chances were he'd come out on top.

As for the Episode the "Wounded" I'm pretty sure we never saw the Phoenix take a hit on-screen (only on a long range sensor graphic) so we don't know what kind of hit that was since even tier 1 Galaxies can take glancing blows without suffering a Warp Core Breach and the Enterprise took several direct hits from Klingon Bird of Prey Disruptor shots and torpedos on bare hull before going down.

[biostem]

Memory Alpha lists the Galors as about 360M long, so a little more than half the length of a Galaxy. Perhaps these were relatively simple ships by Alpha Quadrant standards, (little more than a flying gun), and so the Cardassians could simply field many more of them? Even if they were only 75% as durable as a Galaxy, they could still win by attrition...

[LastShadow]

Or the Cardies are significantly better on the ground than they are in space, and the Feds lack the will or the capacity to root them out.

Certainly possible (though, arguably, a kindergarten class would be better than the Federation on the ground...). I haven't watched enough DS9 to know whether or not the Cardies fought the Feds before the Dominion came onto the scene. It's possible that the Feds simply didn't deploy any serious fighting ships on the scene beforehand, and suffered some losses as a result, and chickened out.

In DS9, O'Brien mentions several times fighting the "damned cardies", and its mentioned I think once in the episode where he is put on trial, that he personally has killed several dozen of them himself, from this I would guess that at some point there was a fed/cardie war. Also this is why the fed/cardie demilitarized zone, and the beginning of the maquis.

[Elheru Aran]

Should have checked Memory Alpha to start with:

http://memory-alpha.wikia.com/wiki/Fede ... assian_War

Starts roughly a couple decades before TNG and ends mid-TNG. Apparently this was after Wolf 359, so perhaps (probably?) one reason the Federation signed a cease-fire was because of the losses there.

EDIT: O'Brien was part of the response to a Cardassian massacre, which led in part to the formation of the Maquis after the cease-fire. Picard's Stargazer encountered a Cardassian ship and was damaged in the battle.