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SONY is that little kid in the playground that smells like piss and doesnt play nice.
While Final Cut does not edit AVCHD natively, it is still a simple procedure to utilize the AVCHD footage. In Final Cut you would open your log and transfer window and import the footage as Pro Res 422 which, while it creates larger files. I suggest you purchsed MTS Convert for Mac, saved your time.
iMovie,FCE converts mts format into the Apple Intermediate Codec...an option that FCP offers as well. FCP defaults to ProRes...which is bigger than AIC.