The Falcon andthe Galactica have an existentialistic, survivalist touch which the Enterprise doesn't (and VOY is rightly criticized for feeling like the Enterprise when it should feel like the Galactica). When the ships go down in TSFS and GEN it is not a matter of life and death, the crew survives without the support of their vessel .
Solo is out of business and thus nothing without his ship and in BSG humankind direly needs their one capital ship. If Picard loses a ship he simply gets another one (well, after some ten year or so captain hiatus).
I think that's why the former two are as Tom described more like characters whereas the Enterprise is as Kevin described more like a mere background.