Making a Big Bad able to impersonate characters can really drive viewers nuts, because you're not sure if they're real or not! I've about had it! I just hope they don't prolong this Giles or not Giles thing until the finale. Why did they have to have that Ax scene with him at the end? Anyway, here's my perspective:
If FE Giles (in Sunnydale) was telling the truth about the FE only taking form of the dead, then Giles IS dead.
If FE Giles was telling a lie about the FE taking form of the dead, then there are two Giles: FE Giles (in Buffy's house) and real Giles (probably still in England). Hence, Giles IS alive.
It's a 50/50 shot so there's really no way of knowing for sure. Then again, they do give Giles certain allowances, since he's the eldest. For instance, whenever someone's tortured on BTVS like Angel or Spike, they're not afraid to show it. However, when Angelus was torturing Giles in Becoming 2, they didn't show it on screen. Hearing him scream in agony would be unbearable. MY POINT is that showing Giles being decapitated on screen would be way too disturbing for an audience, but it doesn't mean that it didn't happen. They show you just enough so that you get the message. So yeah, as much as I hate to say it, he's probably dead.