I'm aware of why using a live CD is sometimes necessary, didn't think that was essential to mention on LWN.
LVM on older kernels (< 2.6.33) that don't fully support write barriers is also rather dangerous for everyday operations, not just filesystem moves/resizes, unless you turn off write caching in the hard drive (long story, search for "lvm risks" in google).
So whether you use LVM or Gparted, you need to ensure your machine doesn't crash, that the moving-stuff-around app doesn't crash (pvmove has been known to cause data loss due to lack of RAM, see my comments elsewhere).
LVM is somewhat safer if you have a good UPS and have correctly configured write barriers and write caches, but since I use UPSes for my PCs and have yet to had a PSU failure or machine crash during a Gparted operation, I'm happy that the risk is quite low.
In fact the one time I lost data with GParted was when not using a live CD - the rather old kernel + Gparted versions meant that the partition table wasn't properly updated and I omitted to reboot. So a live CD is definitely the way to go.
Whatever method you use, you really need to do a full backup anyway, which guards against the sorts of data-loss mentioned here. So it comes down to speed, ease of use, reliability, etc.