Later, in the safety of Kenobi's hovel, Artoo burst out with excitement (and perhaps recognition) upon sighting Anakin's lightsabre.
Right...
In his early conversations with Luke Skywalker, he evaded discussion of Princess Leia until late after key facts were told in Kenobi's presence. When Obi-Wan began to tell Luke a tale about Anakin and the Jedi, Threepio requested to be shut down, likely to avoid discussion and facing awkward memories about his Maker's tragic fate. Nevertheless the supposedly inert droid was only pretending unconsciousness; as he eavesdropped on the conversation he swayed slightly but visibly. This evasive behaviour was prompted by Threepio's recognition of Anakin's lightsabre.
Uh-huh...
For their part, neither droid could be expected to recognise Kenobi (or Owen Lars) in the Tatooine desert after 19 years of aging.
Er...
Vader didn't meet R2-D2 on Bespin, and he might not have cared enough to address C-3PO there. However the fact that he sent C-3PO's parts to Chewbacca's cell for repair could be interpreted as an act of mercy.
But...
C-3PO ought to have remembered his earlier experiences on Tatooine when he returned in A New Hope, yet he seemed unfamiliar with the Dune Sea. Perhaps he had spent most of his early existence in the comfort of the towns and the Lars farm, avoiding the most desolate areas.
Now, hang on...
Later evidence conclusively disproves the "mind-wipe" theories, at least with regard to C-3PO. During preparations for Luke Skywalker's wedding [Union #1], C-3PO declares that "I first met the groom, Master Luke Skywalker, on Tatooine, the planet of my birth." Therefore he does recall his origins with Anakin and Shmi Skywalker. If he rarely speaks of those times, it is because of indifference, absent-mindedness or strict confidentiality.
You can't...
C-3PO is tactful and secretive, and a bit self-centred. R2-D2 is unintelligible to almost everyone except C-3PO. Both droids are common models, and the human characters they dealt with in the prequel era had been wounded or aged beyond recognition by the time Luke Skywalker's adventures began. These two facts explain all of the would-be discontinuities.