As @ChristianRau suggests, this could simply be guilt, or suppressed memory. I think it is possibly both, coupled with the fact that Borden/Fallon are twins. From the voice over as Angier reads Borden's diary:
BORDEN (V.O.) How often I've fought with my self over that night ..
one half of me swearing bling that i tied a simple slip knot... the
other half convinced that I tied the Langford double. I suppose I'll
never know for sure.
It seems clear from how this is written that one of the twins believed that a simple slip knot had been used, the other believed that a Langford double had been used. It seems likely that the twin responsible believed he'd tied the usual knot, but perhaps suppressed the real memory as @ChristianRau suggests. The other twin might understandably believe, as Angier did, that he must have tied the more secure double. This is supposition, but seems a more plausible than the other way around.
So when Angier asks Borden directly, during the funeral, or when performing the bullet-catch - it seems likely that whatever twin is asked, he just was not sure - even the twin that was Borden that night might have doubts even if he started out convinced he had tied the slip knot. This would be even more likely if by coincidence Angier asks the twin who was Fallon that night, so would really not know for sure.