[DirectorTsaarx]

Crew quarters provide a small portion of defense against boarding; therefore, larger ships (with more crew quarters) have more defense against boarding parties. So you either have to use more boarding parties, or damage the ship until some (or all) crew quarters are gone.

And, as Cap'n Kwok mentioned, the target's shields have to be completely down before boarding. Also note that boarding another ship will cause your OWN shields to go down, and they won't come back up unless you have shield regenerators. It's best to use at least some armor on your boarding vessels (along with enough shields to survive long enough to engage the enemy).