As soon as he [Frodo] set foot upon the far bank of Silverlode a strange feeling had come upon him, and it deepened as he walked on into the Naith: it seemed to him that he had stepped over a bridge of time into a corner of the Elder Days, and was -now walking in a world that was no more. In Rivendell there was memory of ancient things; in Lórien the ancient things still lived on in the waking world. Evil had been seen and heard there, sorrow had been known; the Elves feared and distrusted the world outside: wolves were howling on the wood's borders: but on the land of Lórien no shadow lay.
There's definitely a dream quality mood to Lorien. If I remember right, even the passage of time changed there, what seemed a few days was in reality weeks or something.
I think that quote sums it up perfectly. Elrond may remember the First Age, but he was born near the end of that time; Galadriel goes back to Valinor itself, and walked in the light of the Two Trees.
Something else that makes a difference, I think, is that Rivendell acted as a haven for travellers on the East/West Road, the "Last Homely House" west of the Misty Mountains. Lothlorien is a haven for Elves; other races did not often visit there, and therefore the Elves there weren't as comfortable around other races as the Elves in Rivendell would have been.