The question pretty much explains itself. How do the two methods compare? I've always used Assembly PCR but the method is prone to mistakes and I'm curious how it compares to Ligase Chain Reaction (LCR).
I have used both Gibson assembly (what you mean by assembly?) and LCR as replacements for blunt or sticky ended cloning. LCR has, for me, worked better in that a higher proportion of constructs that come out have been assembled correctly and I have noticed no mutations after LCR while I have seen them somewhat often with Gibson.